On the Support of Anomalous Dissipation Measures
By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur a...
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Published in | Journal of mathematical fluid mechanics Vol. 26; no. 4 |
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Language | English |
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2024
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Abstract | By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier–Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler (Drivas and Eyink in Commun Math Phys 359(2):733–763, 2018.
https://doi.org/10.1007/s00220-017-3078-4
; Majda in Am Math Soc 43(281):93, 1983.
https://doi.org/10.1090/memo/0281
) and by recent constructions of dissipative incompressible Euler solutions (Brue and De Lellis in Commun Math Phys 400(3):1507–1533, 2023.
https://doi.org/10.1007/s00220-022-04626-0 624
; Brue et al. in Commun Pure App Anal, 2023), as well as passive scalars (Colombo et al. in Ann PDE 9(2):21–48, 2023.
https://doi.org/10.1007/s40818-023-00162-9
; Drivas et al. in Arch Ration Mech Anal 243(3):1151–1180, 2022.
https://doi.org/10.1007/s00205-021-01736-2
). For
L
t
q
L
x
r
suitable Leray–Hopf solutions of the
d
-
dimensional Navier–Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure
P
s
, which gives
s
=
d
-
2
as soon as the solution lies in the Prodi–Serrin class. In the three-dimensional case, this matches with the Caffarelli–Kohn–Nirenberg partial regularity. |
---|---|
AbstractList | By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier–Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler (Drivas and Eyink in Commun Math Phys 359(2):733–763, 2018.
https://doi.org/10.1007/s00220-017-3078-4
; Majda in Am Math Soc 43(281):93, 1983.
https://doi.org/10.1090/memo/0281
) and by recent constructions of dissipative incompressible Euler solutions (Brue and De Lellis in Commun Math Phys 400(3):1507–1533, 2023.
https://doi.org/10.1007/s00220-022-04626-0 624
; Brue et al. in Commun Pure App Anal, 2023), as well as passive scalars (Colombo et al. in Ann PDE 9(2):21–48, 2023.
https://doi.org/10.1007/s40818-023-00162-9
; Drivas et al. in Arch Ration Mech Anal 243(3):1151–1180, 2022.
https://doi.org/10.1007/s00205-021-01736-2
). For
L
t
q
L
x
r
suitable Leray–Hopf solutions of the
d
-
dimensional Navier–Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure
P
s
, which gives
s
=
d
-
2
as soon as the solution lies in the Prodi–Serrin class. In the three-dimensional case, this matches with the Caffarelli–Kohn–Nirenberg partial regularity. By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier–Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler (Drivas and Eyink in Commun Math Phys 359(2):733–763, 2018. https://doi.org/10.1007/s00220-017-3078-4; Majda in Am Math Soc 43(281):93, 1983. https://doi.org/10.1090/memo/0281) and by recent constructions of dissipative incompressible Euler solutions (Brue and De Lellis in Commun Math Phys 400(3):1507–1533, 2023. https://doi.org/10.1007/s00220-022-04626-0 624; Brue et al. in Commun Pure App Anal, 2023), as well as passive scalars (Colombo et al. in Ann PDE 9(2):21–48, 2023. https://doi.org/10.1007/s40818-023-00162-9; Drivas et al. in Arch Ration Mech Anal 243(3):1151–1180, 2022. https://doi.org/10.1007/s00205-021-01736-2). For LtqLxr suitable Leray–Hopf solutions of the d-dimensional Navier–Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure Ps, which gives s=d-2 as soon as the solution lies in the Prodi–Serrin class. In the three-dimensional case, this matches with the Caffarelli–Kohn–Nirenberg partial regularity. |
Author | Drivas, Theodore D. De Rosa, Luigi Inversi, Marco |
Author_xml | – sequence: 1 givenname: Luigi orcidid: 0000-0002-7157-5114 surname: De Rosa fullname: De Rosa, Luigi email: luigi.derosa@unibas.ch organization: Department Mathematik Und Informatik, Universität Basel – sequence: 2 givenname: Theodore D. surname: Drivas fullname: Drivas, Theodore D. organization: Department of Mathematics, Stony Brook University – sequence: 3 givenname: Marco surname: Inversi fullname: Inversi, Marco organization: Department Mathematik Und Informatik, Universität Basel |
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Cites_doi | 10.1088/1361-6544/ab2f42 10.1007/s00205-023-01954-w 10.1137/16M1104147 10.2140/apde.2022.15.2003 10.1007/s00205-021-01736-2 10.1002/cpa.20262 10.3934/cpaa.2011.10.1011 10.1137/120876447 10.1103/PhysRevA.38.6287 10.1007/s00526-022-02273-w 10.1007/s40818-022-00141-6 10.1137/18M1178864 10.1007/BF00253344 10.1017/S0022112074000711 10.1016/j.physd.2023.133654 10.1017/S0022112062000518 10.1090/memo/0281 10.1137/0505092 10.1007/BF02410664 10.1007/BF01163510 10.1090/proc/16104 10.1007/s00205-020-01603-6 10.1007/s00332-018-9476-8 10.1007/s00205-004-0346-1 10.1007/BF02547354 10.1088/0951-7715/21/6/005 10.4310/PAMQ.2007.v3.n3.a9 10.1007/s00205-018-1250-4 10.1007/s00205-023-01878-5 10.1007/s00208-020-02019-z 10.1007/s00220-022-04626-0 10.1007/s00332-018-9500-z 10.1017/S0022112091001830 10.1088/0951-7715/13/1/312 10.1016/0920-5632(87)90008-9 10.1063/1.864731 10.1512/iumj.2008.57.3312 10.1007/s00220-017-3078-4 10.1002/cpa.3160350604 10.1007/s00205-022-01780-6 10.1103/PhysRevLett.129.124501 10.1098/rspa.1991.0082 10.1063/1.1445422 10.1063/1.869575 10.1007/s40818-023-00162-9 |
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References | CR39 Drivas, Elgindi, Iyer, Jeong (CR18) 2022; 243 CR38 Cheskidov, Shvydkoy (CR12) 2023; 247 CR36 Kolmogorov (CR40) 1962; 13 CR35 Drivas, Eyink (CR19) 2018; 359 Jeong, Yoneda (CR37) 2021; 380 CR33 Meneveau, Sreenivasan (CR50) 1987; 2 Wu (CR66) 2022; 61 CR32 Dubrulle, Gibbon (CR23) 2022; 380 Drivas (CR17) 2019; 29 CR30 Mandelbrot (CR47) 1974; 62 Prodi (CR56) 1959; 4 De Lellis, Kwon (CR14) 2022; 15 Taylor (CR63) 1917; 648 CR2 Shinbrot (CR59) 1974; 5 Sreenivasan (CR62) 1998; 10 Meneveau, Sreenivasan (CR51) 1988; 38 Sohr (CR60) 1983; 184 Duchon, Robert (CR24) 2000; 13 CR48 Isett (CR34) 2022; 244 Chen, Torres, Ziemer (CR8) 2007; 3 Sreenivasan (CR61) 1984; 27 Gibbon (CR31) 2023; 445 CR41 Leslie, Shvydkoy (CR43) 2018; 50 Serrin (CR58) 1962; 9 Colombo, Crippa, Sorella (CR13) 2023; 9 Cheskidov, Shvydkoy (CR11) 2014; 46 Šilhavý (CR64) 2005; 113 Bruè, De Lellis (CR1) 2023; 400 De Rosa, Haffter (CR15) 2023; 151 Phuc, Torres (CR55) 2008; 57 CR57 Chen, Torres, Ziemer (CR9) 2009; 62 Chen, Torres (CR6) 2005; 175 CR53 CR52 Majda (CR46) 1983 Buckmaster, Drivas, Shkoller, Vicol (CR3) 2022; 8 Drivas, Nguyen (CR21) 2018; 50 Leray (CR42) 1934; 63 Leslie, Shvydkoy (CR44) 2018; 230 De Rosa, Isett (CR16) 2024; 248 Caffarelli, Kohn, Nirenberg (CR4) 1982; 35 CR28 CR27 CR26 CR25 Pearson, Krongstad, van de Water (CR54) 2002; 14 Chen, Torres (CR7) 2011; 10 Wu (CR65) 2021; 239 Frisch (CR29) 1991; 434 Cheskidov, Constantin, Friedlander, Shvydkoy (CR10) 2008; 21 Cheminet, Geneste, Barlet, Ostovan, Chaabo, Valori, Debue, Cuvier, Daviaud, Foucaut, Laval, Padilla, Wiertel-Gasquet, Dubrulle (CR5) 2022; 129 Drivas, Eyink (CR20) 2019; 32 Meneveau, Sreenivasan (CR49) 1991; 224 Lions (CR45) 1960; 30 Drivas, Nguyen (CR22) 2019; 29 |
References_xml | – volume: 32 start-page: 4465 issue: 11 year: 2019 end-page: 4482 ident: CR20 article-title: An Onsager singularity theorem for Leray solutions of incompressible Navier-Stokes publication-title: Nonlinearity doi: 10.1088/1361-6544/ab2f42 contributor: fullname: Eyink – volume: 248 start-page: Paper No. 11, 37 issue: 1 year: 2024 ident: CR16 article-title: Intermittency and lower dimensional dissipation in incompressible fluids publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-023-01954-w contributor: fullname: Isett – volume: 50 start-page: 870 issue: 1 year: 2018 end-page: 890 ident: CR43 article-title: Conditions implying energy equality for weak solutions of the Navier-Stokes equations publication-title: SIAM J. Math. Anal. doi: 10.1137/16M1104147 contributor: fullname: Shvydkoy – volume: 15 start-page: 2003 issue: 8 year: 2022 end-page: 2059 ident: CR14 article-title: On nonuniqueness of Hölder continuous globally dissipative Euler flows publication-title: Anal. PDE doi: 10.2140/apde.2022.15.2003 contributor: fullname: Kwon – volume: 243 start-page: 1151 issue: 3 year: 2022 end-page: 1180 ident: CR18 article-title: Anomalous dissipation in passive scalar transport publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-021-01736-2 contributor: fullname: Jeong – ident: CR39 – volume: 62 start-page: 242 issue: 2 year: 2009 end-page: 304 ident: CR9 article-title: Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.20262 contributor: fullname: Ziemer – volume: 10 start-page: 1011 issue: 4 year: 2011 end-page: 1036 ident: CR7 article-title: On the structure of solutions of nonlinear hyperbolic systems of conservation laws publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2011.10.1011 contributor: fullname: Torres – volume: 46 start-page: 353 issue: 1 year: 2014 end-page: 374 ident: CR11 article-title: Euler equations and turbulence: analytical approach to intermittency publication-title: SIAM J. Math. Anal. doi: 10.1137/120876447 contributor: fullname: Shvydkoy – ident: CR35 – volume: 38 start-page: 6287 issue: 12 year: 1988 ident: CR51 article-title: Singularities of the equations of fluid motion publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.38.6287 contributor: fullname: Sreenivasan – volume: 61 start-page: 152 issue: 4 year: 2022 ident: CR66 article-title: Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6 publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s00526-022-02273-w contributor: fullname: Wu – ident: CR25 – volume: 30 start-page: 16 year: 1960 end-page: 23 ident: CR45 article-title: Sur la régularité et l’unicité des solutions turbulentes des équations de Navier Stokes publication-title: Rend. Sem. Mat. Univ. Padova contributor: fullname: Lions – volume: 8 issue: 2 year: 2022 ident: CR3 article-title: Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data publication-title: Ann. PDE doi: 10.1007/s40818-022-00141-6 contributor: fullname: Vicol – volume: 50 start-page: 4785 issue: 5 year: 2018 end-page: 4811 ident: CR21 article-title: Onsager’s conjecture and anomalous dissipation on domains with boundary publication-title: SIAM J. Math. Anal. doi: 10.1137/18M1178864 contributor: fullname: Nguyen – volume: 9 start-page: 187 year: 1962 end-page: 195 ident: CR58 article-title: On the interior regularity of weak solutions of the Navier-Stokes equations publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00253344 contributor: fullname: Serrin – volume: 380 start-page: Paper No. 20210092, 10 issue: 2218 year: 2022 ident: CR23 article-title: A correspondence between the multifractal model of turbulence and the Navier-Stokes equations publication-title: Philos. Trans. Roy. Soc. A contributor: fullname: Gibbon – volume: 62 start-page: 331 issue: 2 year: 1974 end-page: 358 ident: CR47 article-title: Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier publication-title: J. Fluid Mech. doi: 10.1017/S0022112074000711 contributor: fullname: Mandelbrot – volume: 445 start-page: Paper No. 133654, 4 year: 2023 ident: CR31 article-title: Identifying the multifractal set on which energy dissipates in a turbulent Navier-Stokes fluid publication-title: Phys. D doi: 10.1016/j.physd.2023.133654 contributor: fullname: Gibbon – volume: 13 start-page: 82 year: 1962 end-page: 85 ident: CR40 article-title: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number publication-title: J. Fluid Mech. doi: 10.1017/S0022112062000518 contributor: fullname: Kolmogorov – year: 1983 ident: CR46 article-title: The existence of multidimensional shock fronts publication-title: Mem. Am. Math. Soc. doi: 10.1090/memo/0281 contributor: fullname: Majda – ident: CR57 – volume: 5 start-page: 948 year: 1974 end-page: 954 ident: CR59 article-title: The energy equation for the Navier-Stokes system, SIAM publication-title: J. Math. Anal. doi: 10.1137/0505092 contributor: fullname: Shinbrot – volume: 648 start-page: 99 year: 1917 end-page: 113 ident: CR63 article-title: Motion of solids in fluids when the flow is not irrotational publication-title: Proc. R. Soc. A contributor: fullname: Taylor – ident: CR32 – volume: 4 start-page: 173 issue: 48 year: 1959 end-page: 182 ident: CR56 article-title: Un teorema di unicità per le equazioni di Navier-Stokes publication-title: Ann. Mat. Pura Appl. doi: 10.1007/BF02410664 contributor: fullname: Prodi – ident: CR36 – volume: 184 start-page: 359 issue: 3 year: 1983 end-page: 375 ident: CR60 article-title: Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes, German publication-title: Math. Z. doi: 10.1007/BF01163510 contributor: fullname: Sohr – volume: 151 start-page: 255 issue: 1 year: 2023 end-page: 267 ident: CR15 article-title: A fractal version of the Onsager’s conjecture: the model publication-title: Proc. Amer. Math. Soc. doi: 10.1090/proc/16104 contributor: fullname: Haffter – ident: CR26 – volume: 239 start-page: 1771 issue: 3 year: 2021 end-page: 1808 ident: CR65 article-title: Partially regular weak solutions of the Navier-Stokes equations in publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-020-01603-6 contributor: fullname: Wu – volume: 29 start-page: 65 issue: 1 year: 2019 end-page: 88 ident: CR17 article-title: Turbulent cascade direction and Lagrangian time-asymmetry publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-018-9476-8 contributor: fullname: Drivas – volume: 175 start-page: 245 issue: 2 year: 2005 end-page: 267 ident: CR6 article-title: Divergence-measure fields, sets of finite perimeter, and conservation laws publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-004-0346-1 contributor: fullname: Torres – volume: 63 start-page: 193 issue: 1 year: 1934 end-page: 248 ident: CR42 article-title: Sur le mouvement d’un liquide visqueux emplissant l’espace publication-title: Acta Math. doi: 10.1007/BF02547354 contributor: fullname: Leray – ident: CR2 – ident: CR53 – ident: CR30 – volume: 21 start-page: 1233 issue: 6 year: 2008 end-page: 1252 ident: CR10 article-title: Energy conservation and Onsager’s conjecture for the Euler equations publication-title: Nonlinearity doi: 10.1088/0951-7715/21/6/005 contributor: fullname: Shvydkoy – volume: 3 start-page: 841 issue: 3, Special Issue: In honor of Leon Simon. Part 2 year: 2007 end-page: 879 ident: CR8 article-title: Measure-theoretic analysis and nonlinear conservation laws publication-title: Pure Appl. Math. Q. doi: 10.4310/PAMQ.2007.v3.n3.a9 contributor: fullname: Ziemer – ident: CR33 – volume: 230 start-page: 459 issue: 2 year: 2018 end-page: 492 ident: CR44 article-title: The energy measure for the Euler and Navier-Stokes equations publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-018-1250-4 contributor: fullname: Shvydkoy – volume: 247 start-page: Paper No. 45, 35 issue: 3 year: 2023 ident: CR12 article-title: Volumetric theory of intermittency in fully developed turbulence publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-023-01878-5 contributor: fullname: Shvydkoy – ident: CR27 – volume: 380 start-page: 2041 issue: 3–4 year: 2021 end-page: 2072 ident: CR37 article-title: Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations publication-title: Math. Ann. doi: 10.1007/s00208-020-02019-z contributor: fullname: Yoneda – volume: 400 start-page: 1507 issue: 3 year: 2023 end-page: 1533 ident: CR1 article-title: Anomalous dissipation for the forced 3D Navier-Stokes equations publication-title: Comm. Math. Phys. doi: 10.1007/s00220-022-04626-0 contributor: fullname: De Lellis – volume: 29 start-page: 709 issue: 2 year: 2019 end-page: 721 ident: CR22 article-title: Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-018-9500-z contributor: fullname: Nguyen – ident: CR48 – volume: 224 start-page: 429 year: 1991 end-page: 484 ident: CR49 article-title: The multifractal nature of turbulent energy dissipation publication-title: J. Fluid Mech. doi: 10.1017/S0022112091001830 contributor: fullname: Sreenivasan – volume: 13 start-page: 249 issue: 1 year: 2000 end-page: 255 ident: CR24 article-title: Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations publication-title: Nonlinearity doi: 10.1088/0951-7715/13/1/312 contributor: fullname: Robert – ident: CR38 – volume: 2 start-page: 49 year: 1987 end-page: 76 ident: CR50 article-title: The multifractal spectrum of the dissipation field in turbulent flows publication-title: Nuclear Phys. B-Proc. Supplements doi: 10.1016/0920-5632(87)90008-9 contributor: fullname: Sreenivasan – ident: CR52 – volume: 27 start-page: 1048 year: 1984 end-page: 1051 ident: CR61 article-title: On the scaling of the turbulence energy dissipation rate publication-title: Phys. Fluids doi: 10.1063/1.864731 contributor: fullname: Sreenivasan – volume: 57 start-page: 1573 issue: 4 year: 2008 end-page: 1597 ident: CR55 article-title: Characterizations of the existence and removable singularities of divergence-measure vector fields publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.2008.57.3312 contributor: fullname: Torres – volume: 359 start-page: 733 issue: 2 year: 2018 end-page: 763 ident: CR19 article-title: An Onsager singularity theorem for turbulent solutions of compressible Euler equations publication-title: Comm. Math. Phys. doi: 10.1007/s00220-017-3078-4 contributor: fullname: Eyink – volume: 35 start-page: 771 issue: 6 year: 1982 end-page: 831 ident: CR4 article-title: Partial regularity of suitable weak solutions of the Navier-Stokes equations publication-title: Comm. Pure Appl. Math. doi: 10.1002/cpa.3160350604 contributor: fullname: Nirenberg – volume: 244 start-page: 1223 issue: 3 year: 2022 end-page: 1309 ident: CR34 article-title: Nonuniqueness and existence of continuous, globally dissipative Euler flows publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-022-01780-6 contributor: fullname: Isett – volume: 129 year: 2022 ident: CR5 article-title: Eulerian vs Lagrangian Irreversibility in an experimental turbulent swirling flow publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.129.124501 contributor: fullname: Dubrulle – volume: 434 start-page: 89 year: 1991 end-page: 99 ident: CR29 article-title: From global scaling, à la Kolmogorov publication-title: To local multifractal scaling in fully developed turbulence doi: 10.1098/rspa.1991.0082 contributor: fullname: Frisch – volume: 14 start-page: 1288 year: 2002 end-page: 1290 ident: CR54 article-title: Measurements of the turbulent energy dissipation rate publication-title: Phys. Fluids doi: 10.1063/1.1445422 contributor: fullname: van de Water – ident: CR28 – ident: CR41 – volume: 10 start-page: 528 issue: 2 year: 1998 end-page: 529 ident: CR62 article-title: An update on the energy dissipation rate in isotropic turbulence publication-title: Phys. Fluids doi: 10.1063/1.869575 contributor: fullname: Sreenivasan – volume: 9 start-page: Paper No. 21, 48 issue: 2 year: 2023 ident: CR13 article-title: Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence publication-title: Ann. PDE doi: 10.1007/s40818-023-00162-9 contributor: fullname: Sorella – volume: 113 start-page: 15 year: 2005 end-page: 45 ident: CR64 article-title: Divergence measure fields and Cauchy’s stress theorem publication-title: Rend. Sem. Mat. Univ. Padova contributor: fullname: Šilhavý |
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SubjectTerms | Classical and Continuum Physics Compressibility Dissipation Fluid flow Fluid- and Aerodynamics Incompressible flow Lower bounds Mathematical Methods in Physics Navier-Stokes equations Physics Physics and Astronomy Scalars |
Title | On the Support of Anomalous Dissipation Measures |
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