Convergence to equilibria for compressible Navier-Stokes equations with large data
type: Item
instance of: scholarly article
title: Convergence to equilibria for compressible Navier-Stokes equations with large data
zbMATH Open document ID: 1038.76037
DOI: 10.1007/BF02505958
author: Antonín Novotný
author: I. Straškraba
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2003-10-19T00:00:00Z
review text: This paper studies the large-time behavior of solutions to an initial-boundary value problem with periodic boundary conditions for compressible barotropic Navier-Stokes equations in \(\mathbb{R}^n\) (\(n=2,3\)). Assuming that the external force is potential and that the pressure satisfies certain conditions (e.g., in the isentropic case, the specific heat ratio \(\gamma >6/5\) for \(n=2\) and \(\gamma >3/2\) for \(n=3\)), the authors prove that for any sequence \(t_n\to\infty\) and any global (renormalized) weak solution \((\rho ,u)\) there is a subsequence \(\{s_n\}\) such that \(\rho (s_n)\to\rho_\infty\) in the space \(L^r_\omega (\Omega)\) of spatially periodic functions, \(r>1\) suitable, where \(\rho_\infty\) is an equilibrium density. Moreover, if the equilibrium is unique, then \(\rho (t)\to\rho_\infty\) in \(L^r_\omega (\Omega)\) as \(t\to\infty\). The main ingredients in the proof are careful and tricky a priori estimates and the exploitation of the energy estimate established for weak solutions.
reviewed by: Song Jiang
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1993715
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: periodic boundary condition
zbMATH Keywords: global weak solution
zbMATH Keywords: equilibrium density
zbMATH Keywords: a priori estimates
zbMATH Keywords: energy estimate
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1993715