Some regularity criteria for the 3D generalized Navier–Stokes equations

We show some regularity criteria (Prodi–Serrin type regularity) to weak solutions of the 3D generalized Navier–Stokes equations in viewpoint of the velocity vector u or the vorticity vector ω : = ∇ × u in Lorentz space. Moreover, we briefly mention some results for coupled equations with Navier–Stok...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 72; no. 3
Main Author Kim, Jae-Myoung
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Subjects
Criteria
Engineering
Fluid dynamics
Fluid flow
Mathematical analysis
Mathematical Methods in Physics
Navier-Stokes equations
Regularity
Theoretical and Applied Mechanics
Vorticity
35B65
76D05
Generalized Navier–Stokes equation
Fractional dissipation
Regularity
35Q35
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Summary:We show some regularity criteria (Prodi–Serrin type regularity) to weak solutions of the 3D generalized Navier–Stokes equations in viewpoint of the velocity vector u or the vorticity vector ω : = ∇ × u in Lorentz space. Moreover, we briefly mention some results for coupled equations with Navier–Stokes equation (see Remark 1.5 and 1.8 ).
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-021-01549-z