Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: II. Serrin-Type Solutions

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Autore principale:	Mikhailov, Sergey E.
Natura:	Preprint
Pubblicazione:	2024
Soggetti:	Analysis of PDEs 35A1, 35B10, 35K45, 35Q30, 76D05
Accesso online:	Acceder al recurso
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author	Mikhailov, Sergey E.
author_facet	Mikhailov, Sergey E.
contents	We consider evolution (non-stationary) space-periodic solutions to the $n$-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm, we prove the existence of Serrin-type solutions, that is, weak solutions with the velocity in the periodic space $L_2(0,T;\dot{\mathbf H}^{n/2}_{\#σ})$, $n\ge 2$. The solution uniqueness and regularity results are also discussed.
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_05488
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: II. Serrin-Type Solutions Mikhailov, Sergey E. Analysis of PDEs 35A1, 35B10, 35K45, 35Q30, 76D05 We consider evolution (non-stationary) space-periodic solutions to the $n$-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm, we prove the existence of Serrin-type solutions, that is, weak solutions with the velocity in the periodic space $L_2(0,T;\dot{\mathbf H}^{n/2}_{\#σ})$, $n\ge 2$. The solution uniqueness and regularity results are also discussed.
title	Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: II. Serrin-Type Solutions
topic	Analysis of PDEs 35A1, 35B10, 35K45, 35Q30, 76D05
url	https://arxiv.org/abs/2407.05488

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