Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system
type: Item
instance of: scholarly article
title: Strong solutions and weak-strong uniqueness for the nonhomogeneous Navier-Stokes system
zbMATH Open document ID: 1198.35179
author: P. Germain
published in: Journal d'Analyse Mathématique
publication date: 2008-10-16T00:00:00Z
review text: The author studies the non-homogeneous incompressible Navier-Stokes system in space. The system describes the evolution of an incompressible viscous fluid whose density is non-constant. The author considers new a priori estimates which enable to deal with low-regularity data and vanishing density. In the paper, new well-posedness results improving previous results of Danchin by considering a less regular initial density are obtained. Furthermore, it is obtained the first uniqueness criterion for weak solutions which is at the scaling of the equation. To do so, the author gives a theorem on the existence of local strong solutions, in which no compatibility condition is required and the density does not have to be bounded from below. In addition, a theorem giving a criterion for the uniqueness of energy class solutions is given.
reviewed by: Mariano Rodríguez Ricard
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 5351760
zbMATH Keywords: non-homogeneous Navier-Stokes equations
zbMATH Keywords: incompressible viscous fluid
zbMATH Keywords: a priori estimates
zbMATH Keywords: Gronwall inequalities
MaRDI profile type: Publication
full work available at URL: s11854-008-0034-4
OpenAlex ID: W2034366757
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DOI: 10.1007/S11854-008-0034-4
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description: scientific article; zbMATH DE number 5351760