Existence of solutions for the compressible Navier-Stokes equations
type: Item
instance of: scholarly article
title: Existence of solutions for the compressible Navier-Stokes equations
zbMATH Open document ID: 0861.35076
published in: Chinese Science Bulletin
publication date: 1996-10-31T00:00:00Z
review text: The author considers the initial value problem for the compressible, isentropic Navier-Stokes equations, i.e. \[ \rho_t+\text{div}(\rho u)=0,\;u_t-\rho^{-1}\mu\Delta u-\rho^{-1}(\mu+\mu')\nabla\text{ div }u+(u\cdot\nabla)u+\rho^{-1}\nabla p(\rho)=0\text{ in }\mathbb{R}^n\times(0,T), \] \[ \rho(.,0)=\overline\rho+\widetilde\rho_0,\quad u(.,0)=u_0\quad\text{in }\mathbb{R}^n, \] where \(n\geq 2\), \(\mu>0\), \(\mu'+{2\over 3}\mu\geq 0\), \(p'(\rho)>0\) and \(\overline\rho>0\) is a constant. He proves local existence of a strong solution and -- under the condition that \(\rho\geq K>0\) -- determines which norm blows up if the strong solution does not exist globally in time.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 940893
zbMATH Keywords: compressible Navier-Stokes equations
zbMATH Keywords: strong solution
zbMATH Keywords: paraproduct
author: Huicheng Yin
reviewed by: Klaus Deckelnick
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 940893