Global strong solutions to the incompressible Navier-Stokes equations with density-dependent viscosity
type: Item
instance of: scholarly article
title: Global strong solutions to the incompressible Navier-Stokes equations with density-dependent viscosity
zbMATH Open document ID: 1351.35107
author: Peixin Zhang
author: Haibo Yu
published in: Journal of Mathematical Analysis and Applications
publication date: 2016-07-29T00:00:00Z
review text: The 3D incompressible Navier-Stokes equations are studied, when the fluid viscosity is depending on the density, in a smooth domain. When the mass of fluid or the density are small enough, the authors obtain the well-posedness of the strong solutions. When the vacuum is allowed, the compatibility condition (1.4), introduced in [\textit{Y. Cho} and \textit{H. Kim}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 4, 465--489 (2004; Zbl 1066.35070)] is used. The norm of the viscosity gradient in a Sobolev space \(L^q\) is considered bounded. This hypothesis allows the use of some regularity results for Stokes equations.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35D35
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6607794
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: incompressible fluids
zbMATH Keywords: density-dependent viscosity
zbMATH Keywords: global strong solutions
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: j.jmaa.2016.06.066
OpenAlex ID: W2466553005
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DOI: 10.1016/J.JMAA.2016.06.066
description: scientific article; zbMATH DE number 6607794