Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations
Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. Perturbations of this kind oscillate in the far field and a...
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| Published in | Journal of Differential Equations Vol. 346; pp. 254 - 276 |
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| Format | Journal Article |
| Language | English |
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| Abstract | Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. Perturbations of this kind oscillate in the far field and are not integrable. The key is to construct a suitable ansatz carrying the same oscillation as that of the initial data, but due to the degeneration of contact discontinuity, the construction is more subtle. A novel method for constructing robust ansatzes is presented. It allows the same weight function to be used on different variables and wave patterns while maintaining control over the errors. As a result, it is possible to apply this construction to contact discontinuities and composite waves. Lastly, we demonstrate that the Cauchy problem admits a unique global-in-time solution and the composite wave remains stable under space-periodic perturbations through the energy method. |
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| AbstractList | Considering the space-periodic perturbations, we prove the time-asymptotic stability of the composite wave of a viscous contact wave and two rarefaction waves for the Cauchy problem of 1-D compressible Navier-Stokes equations in this paper. Perturbations of this kind oscillate in the far field and are not integrable. The key is to construct a suitable ansatz carrying the same oscillation as that of the initial data, but due to the degeneration of contact discontinuity, the construction is more subtle. A novel method for constructing robust ansatzes is presented. It allows the same weight function to be used on different variables and wave patterns while maintaining control over the errors. As a result, it is possible to apply this construction to contact discontinuities and composite waves. Lastly, we demonstrate that the Cauchy problem admits a unique global-in-time solution and the composite wave remains stable under space-periodic perturbations through the energy method. |
| Author | Xu, Lingda Wang, Danli Liu, Lingjun |
| Author_xml | – sequence: 1 givenname: Lingjun orcidid: 0000-0002-8002-2255 surname: Liu fullname: Liu, Lingjun email: lingjunliu@bjut.edu.cn organization: Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, PR China – sequence: 2 givenname: Danli surname: Wang fullname: Wang, Danli email: wangdanli19@amss.ac.cn organization: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China – sequence: 3 givenname: Lingda orcidid: 0000-0002-2982-2994 surname: Xu fullname: Xu, Lingda email: xulingda@tsinghua.edu.cn organization: Department of Mathematics, Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, PR China |
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| Cites_doi | 10.1512/iumj.2021.70.8706 10.1512/iumj.2016.65.5914 10.1002/cpa.3160100406 10.1137/17M1150888 10.1007/s00205-005-0380-7 10.1016/0362-546X(77)90032-3 10.3792/pjaa.62.249 10.1137/18M1192883 10.1016/j.jde.2019.11.008 10.1007/s00220-021-04203-x 10.1007/s00205-009-0267-0 10.1007/BF00276840 10.4310/MAA.2021.v28.n3.a6 10.1016/j.aim.2008.06.014 10.1007/BF03167036 10.1007/BF03167088 10.1137/S003614100342735X 10.1002/mma.4198 10.1016/j.aim.2022.108452 10.4310/AJM.1997.v1.n1.a3 10.1137/21M1408087 10.1007/s00220-009-0843-z |
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| References | Matsumura, Nishihara (br0190) 1986; 3 Ruan, Yin, Zhu (br0210) 2017; 40 Lax (br0150) 1957; 10 Matsumura, Nishihara (br0180) 1985; 2 Xin (br0250) 1996 Goodman (br0020) 1986; 95 Yuan, Yuan (br0240) 2020; 268 Huang, Matsumura (br0040) 2009; 289 Liu, Xin (br0170) 1997; 1 Huang, Matsumura, Xin (br0060) 2006; 179 Huang, Yuan (br0120) 2021; 387 Yuan, Yuan (br0290) 2020; 268 Glimm, Lax (br0010) 1970; vol. 101 Huang, Xin, Yang (br0090) 2008; 219 Li, Wang, Wang (br0160) 2018; 50 Xin, Yuan, Yuan (br0260) 2019; 51 Xin, Yuan, Yuan (br0270) 2021; 70 Huang, Yuan (br0110) 2021; 28 Huang, Li, Matsumura (br0070) 2010; 197 Yao, Zhu (br0280) 2021; 53 Huang, Wang (br0080) 2016; 65 van Duyn, Peletier (br0230) 1976/77; 1 Smoller (br0220) 1994 Kang, Vasseur, Wang (br0130) Huang, Xu, Yuan (br0100) 2022; 404 Nishihara, Yang, Zhao (br0200) 2004; 35 Kawashima, Matsumura, Nishihara (br0140) 1986; 62 Huang, Matsumura, Shi (br0050) 2004; 41 Hsiao, Liu (br0030) 1993; 14 Huang (10.1016/j.jde.2022.11.040_br0110) 2021; 28 Huang (10.1016/j.jde.2022.11.040_br0060) 2006; 179 Kawashima (10.1016/j.jde.2022.11.040_br0140) 1986; 62 Li (10.1016/j.jde.2022.11.040_br0160) 2018; 50 Ruan (10.1016/j.jde.2022.11.040_br0210) 2017; 40 Huang (10.1016/j.jde.2022.11.040_br0080) 2016; 65 Matsumura (10.1016/j.jde.2022.11.040_br0180) 1985; 2 Huang (10.1016/j.jde.2022.11.040_br0100) 2022; 404 Yao (10.1016/j.jde.2022.11.040_br0280) 2021; 53 Xin (10.1016/j.jde.2022.11.040_br0250) 1996 Huang (10.1016/j.jde.2022.11.040_br0050) 2004; 41 Hsiao (10.1016/j.jde.2022.11.040_br0030) 1993; 14 Glimm (10.1016/j.jde.2022.11.040_br0010) 1970; vol. 101 Lax (10.1016/j.jde.2022.11.040_br0150) 1957; 10 Smoller (10.1016/j.jde.2022.11.040_br0220) 1994 Huang (10.1016/j.jde.2022.11.040_br0040) 2009; 289 Yuan (10.1016/j.jde.2022.11.040_br0240) 2020; 268 Xin (10.1016/j.jde.2022.11.040_br0260) 2019; 51 Xin (10.1016/j.jde.2022.11.040_br0270) 2021; 70 Goodman (10.1016/j.jde.2022.11.040_br0020) 1986; 95 Huang (10.1016/j.jde.2022.11.040_br0090) 2008; 219 Matsumura (10.1016/j.jde.2022.11.040_br0190) 1986; 3 Nishihara (10.1016/j.jde.2022.11.040_br0200) 2004; 35 Kang (10.1016/j.jde.2022.11.040_br0130) Yuan (10.1016/j.jde.2022.11.040_br0290) 2020; 268 Huang (10.1016/j.jde.2022.11.040_br0070) 2010; 197 van Duyn (10.1016/j.jde.2022.11.040_br0230) 1976; 1 Huang (10.1016/j.jde.2022.11.040_br0120) 2021; 387 Liu (10.1016/j.jde.2022.11.040_br0170) 1997; 1 |
| References_xml | – volume: 41 start-page: 193 year: 2004 end-page: 210 ident: br0050 article-title: On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary publication-title: Osaka J. Math. contributor: fullname: Shi – volume: 197 start-page: 89 year: 2010 end-page: 116 ident: br0070 article-title: Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system publication-title: Arch. Ration. Mech. Anal. contributor: fullname: Matsumura – year: 1994 ident: br0220 article-title: Shock Waves and Reaction-Diffusion Equations contributor: fullname: Smoller – volume: 51 start-page: 2971 year: 2019 end-page: 2994 ident: br0260 article-title: Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws publication-title: SIAM J. Math. Anal. contributor: fullname: Yuan – volume: 404 year: 2022 ident: br0100 article-title: Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations publication-title: Adv. Math. contributor: fullname: Yuan – volume: 219 start-page: 1246 year: 2008 end-page: 1297 ident: br0090 article-title: Contact discontinuity with general perturbations for gas motions publication-title: Adv. Math. contributor: fullname: Yang – volume: 10 start-page: 537 year: 1957 end-page: 566 ident: br0150 article-title: Hyperbolic systems of conservation laws ii publication-title: Commun. Pure Appl. Math. contributor: fullname: Lax – start-page: 249 year: 1996 end-page: 257 ident: br0250 article-title: On nonlinear stability of contact discontinuities publication-title: Hyperbolic Problems: Theory, Numerics, Applications contributor: fullname: Xin – volume: 268 start-page: 5140 year: 2020 end-page: 5155 ident: br0240 article-title: On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws publication-title: J. Differ. Equ. contributor: fullname: Yuan – volume: 268 start-page: 5140 year: 2020 end-page: 5155 ident: br0290 article-title: On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws publication-title: J. Differ. Equ. contributor: fullname: Yuan – volume: 179 start-page: 55 year: 2006 end-page: 77 ident: br0060 article-title: Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations publication-title: Arch. Ration. Mech. Anal. contributor: fullname: Xin – volume: 387 start-page: 1655 year: 2021 end-page: 1679 ident: br0120 article-title: Stability of large-amplitude viscous shock under periodic perturbation for 1-D isentropic Navier-Stokes equations publication-title: Commun. Math. Phys. contributor: fullname: Yuan – volume: 65 start-page: 1833 year: 2016 end-page: 1875 ident: br0080 article-title: Stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system publication-title: Indiana Univ. Math. J. contributor: fullname: Wang – volume: 95 start-page: 325 year: 1986 end-page: 344 ident: br0020 article-title: Nonlinear asymptotic stability of viscous shock profiles for conservation laws publication-title: Arch. Ration. Mech. Anal. contributor: fullname: Goodman – volume: 28 start-page: 337 year: 2021 end-page: 353 ident: br0110 article-title: Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations publication-title: Methods Appl. Anal. contributor: fullname: Yuan – volume: 1 start-page: 34 year: 1997 end-page: 84 ident: br0170 article-title: Pointwise decay to contact discontinuities for systems of viscous conservation laws publication-title: Asian J. Math. contributor: fullname: Xin – volume: 40 start-page: 2784 year: 2017 end-page: 2810 ident: br0210 article-title: Stability of the superposition of rarefaction wave and contact discontinuity for the non-isentropic Navier-Stokes-Poisson system publication-title: Math. Methods Appl. Sci. contributor: fullname: Zhu – volume: 289 start-page: 841 year: 2009 end-page: 861 ident: br0040 article-title: Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation publication-title: Commun. Math. Phys. contributor: fullname: Matsumura – volume: 53 start-page: 6122 year: 2021 end-page: 6163 ident: br0280 article-title: Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations publication-title: SIAM J. Math. Anal. contributor: fullname: Zhu – volume: 3 start-page: 1 year: 1986 end-page: 13 ident: br0190 article-title: Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas publication-title: Jpn. J. Appl. Math. contributor: fullname: Nishihara – volume: 2 start-page: 17 year: 1985 end-page: 25 ident: br0180 article-title: On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas publication-title: Jpn. J. Appl. Math. contributor: fullname: Nishihara – volume: 70 start-page: 2295 year: 2021 end-page: 2349 ident: br0270 article-title: Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws publication-title: Indiana Univ. Math. J. contributor: fullname: Yuan – volume: vol. 101 year: 1970 ident: br0010 article-title: Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws publication-title: Memoirs of the American Mathematical Society contributor: fullname: Lax – volume: 14 start-page: 465 year: 1993 end-page: 480 ident: br0030 article-title: Nonlinear diffusive phenomena of nonlinear hyperbolic systems publication-title: Chin. Ann. Math., Ser. B contributor: fullname: Liu – ident: br0130 article-title: Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations contributor: fullname: Wang – volume: 62 start-page: 249 year: 1986 end-page: 252 ident: br0140 article-title: Asymptotic behavior of solutions for the equations of a viscous heat-conductive gas publication-title: Proc. Jpn. Acad., Ser. A, Math. Sci. contributor: fullname: Nishihara – volume: 50 start-page: 1829 year: 2018 end-page: 1876 ident: br0160 article-title: Stability of the superposition of a viscous contact wave with two rarefaction waves to the bipolar Vlasov-Poisson-Boltzmann system publication-title: SIAM J. Math. Anal. contributor: fullname: Wang – volume: 35 start-page: 1561 year: 2004 end-page: 1597 ident: br0200 article-title: Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equation publication-title: SIAM J. Math. Anal. contributor: fullname: Zhao – volume: 1 start-page: 223 year: 1976/77 end-page: 233 ident: br0230 article-title: A class of similarity solutions of the nonlinear diffusion equation publication-title: Nonlinear Anal. contributor: fullname: Peletier – volume: 70 start-page: 2295 issue: 6 year: 2021 ident: 10.1016/j.jde.2022.11.040_br0270 article-title: Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.2021.70.8706 contributor: fullname: Xin – volume: 65 start-page: 1833 issue: 6 year: 2016 ident: 10.1016/j.jde.2022.11.040_br0080 article-title: Stability of superposition of viscous contact wave and rarefaction waves for compressible Navier-Stokes system publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.2016.65.5914 contributor: fullname: Huang – volume: 10 start-page: 537 issue: 4 year: 1957 ident: 10.1016/j.jde.2022.11.040_br0150 article-title: Hyperbolic systems of conservation laws ii publication-title: Commun. Pure Appl. Math. doi: 10.1002/cpa.3160100406 contributor: fullname: Lax – volume: 50 start-page: 1829 issue: 2 year: 2018 ident: 10.1016/j.jde.2022.11.040_br0160 article-title: Stability of the superposition of a viscous contact wave with two rarefaction waves to the bipolar Vlasov-Poisson-Boltzmann system publication-title: SIAM J. Math. Anal. doi: 10.1137/17M1150888 contributor: fullname: Li – volume: 179 start-page: 55 year: 2006 ident: 10.1016/j.jde.2022.11.040_br0060 article-title: Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-005-0380-7 contributor: fullname: Huang – volume: vol. 101 year: 1970 ident: 10.1016/j.jde.2022.11.040_br0010 article-title: Decay of Solutions of Systems of Nonlinear Hyperbolic Conservation Laws contributor: fullname: Glimm – volume: 1 start-page: 223 issue: 3 year: 1976 ident: 10.1016/j.jde.2022.11.040_br0230 article-title: A class of similarity solutions of the nonlinear diffusion equation publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(77)90032-3 contributor: fullname: van Duyn – volume: 41 start-page: 193 year: 2004 ident: 10.1016/j.jde.2022.11.040_br0050 article-title: On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary publication-title: Osaka J. Math. contributor: fullname: Huang – volume: 62 start-page: 249 issue: 7 year: 1986 ident: 10.1016/j.jde.2022.11.040_br0140 article-title: Asymptotic behavior of solutions for the equations of a viscous heat-conductive gas publication-title: Proc. Jpn. Acad., Ser. A, Math. Sci. doi: 10.3792/pjaa.62.249 contributor: fullname: Kawashima – volume: 51 start-page: 2971 issue: 4 year: 2019 ident: 10.1016/j.jde.2022.11.040_br0260 article-title: Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws publication-title: SIAM J. Math. Anal. doi: 10.1137/18M1192883 contributor: fullname: Xin – volume: 268 start-page: 5140 issue: 9 year: 2020 ident: 10.1016/j.jde.2022.11.040_br0240 article-title: On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2019.11.008 contributor: fullname: Yuan – volume: 14 start-page: 465 year: 1993 ident: 10.1016/j.jde.2022.11.040_br0030 article-title: Nonlinear diffusive phenomena of nonlinear hyperbolic systems publication-title: Chin. Ann. Math., Ser. B contributor: fullname: Hsiao – volume: 387 start-page: 1655 issue: 3 year: 2021 ident: 10.1016/j.jde.2022.11.040_br0120 article-title: Stability of large-amplitude viscous shock under periodic perturbation for 1-D isentropic Navier-Stokes equations publication-title: Commun. Math. Phys. doi: 10.1007/s00220-021-04203-x contributor: fullname: Huang – ident: 10.1016/j.jde.2022.11.040_br0130 contributor: fullname: Kang – start-page: 249 year: 1996 ident: 10.1016/j.jde.2022.11.040_br0250 article-title: On nonlinear stability of contact discontinuities contributor: fullname: Xin – volume: 197 start-page: 89 year: 2010 ident: 10.1016/j.jde.2022.11.040_br0070 article-title: Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier-Stokes system publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-009-0267-0 contributor: fullname: Huang – volume: 268 start-page: 5140 issue: 9 year: 2020 ident: 10.1016/j.jde.2022.11.040_br0290 article-title: On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2019.11.008 contributor: fullname: Yuan – volume: 95 start-page: 325 year: 1986 ident: 10.1016/j.jde.2022.11.040_br0020 article-title: Nonlinear asymptotic stability of viscous shock profiles for conservation laws publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00276840 contributor: fullname: Goodman – volume: 28 start-page: 337 issue: 3 year: 2021 ident: 10.1016/j.jde.2022.11.040_br0110 article-title: Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations publication-title: Methods Appl. Anal. doi: 10.4310/MAA.2021.v28.n3.a6 contributor: fullname: Huang – volume: 219 start-page: 1246 year: 2008 ident: 10.1016/j.jde.2022.11.040_br0090 article-title: Contact discontinuity with general perturbations for gas motions publication-title: Adv. Math. doi: 10.1016/j.aim.2008.06.014 contributor: fullname: Huang – volume: 2 start-page: 17 issue: 1 year: 1985 ident: 10.1016/j.jde.2022.11.040_br0180 article-title: On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas publication-title: Jpn. J. Appl. Math. doi: 10.1007/BF03167036 contributor: fullname: Matsumura – volume: 3 start-page: 1 year: 1986 ident: 10.1016/j.jde.2022.11.040_br0190 article-title: Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas publication-title: Jpn. J. Appl. Math. doi: 10.1007/BF03167088 contributor: fullname: Matsumura – volume: 35 start-page: 1561 issue: 6 year: 2004 ident: 10.1016/j.jde.2022.11.040_br0200 article-title: Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equation publication-title: SIAM J. Math. Anal. doi: 10.1137/S003614100342735X contributor: fullname: Nishihara – volume: 40 start-page: 2784 issue: 7 year: 2017 ident: 10.1016/j.jde.2022.11.040_br0210 article-title: Stability of the superposition of rarefaction wave and contact discontinuity for the non-isentropic Navier-Stokes-Poisson system publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.4198 contributor: fullname: Ruan – year: 1994 ident: 10.1016/j.jde.2022.11.040_br0220 contributor: fullname: Smoller – volume: 404 year: 2022 ident: 10.1016/j.jde.2022.11.040_br0100 article-title: Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations publication-title: Adv. Math. doi: 10.1016/j.aim.2022.108452 contributor: fullname: Huang – volume: 1 start-page: 34 issue: 1 year: 1997 ident: 10.1016/j.jde.2022.11.040_br0170 article-title: Pointwise decay to contact discontinuities for systems of viscous conservation laws publication-title: Asian J. Math. doi: 10.4310/AJM.1997.v1.n1.a3 contributor: fullname: Liu – volume: 53 start-page: 6122 issue: 5 year: 2021 ident: 10.1016/j.jde.2022.11.040_br0280 article-title: Asymptotic stability of the superposition of viscous contact wave with rarefaction waves for the compressible Navier-Stokes-Maxwell equations publication-title: SIAM J. Math. Anal. doi: 10.1137/21M1408087 contributor: fullname: Yao – volume: 289 start-page: 841 year: 2009 ident: 10.1016/j.jde.2022.11.040_br0040 article-title: Stability of a composite wave of two viscous shock waves for the full compressible Navier-Stokes equation publication-title: Commun. Math. Phys. doi: 10.1007/s00220-009-0843-z contributor: fullname: Huang |
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| Title | Asymptotic stability of the combination of a viscous contact wave with two rarefaction waves for 1-D Navier-Stokes equations under periodic perturbations |
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