Global existence of solutions to the compressible Navier-Stokes equation around parallel flows

Yoshiyuki Kagei

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8 Citations (Scopus)

Abstract

The initial boundary value problem for the compressible Navier-Stokes equation is considered in an infinite layer of Rn. It is proved that if n≥3, then strong solutions to the compressible Navier-Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations, provided that the Reynolds and Mach numbers are sufficiently small. The proof is given by a variant of the Matsumura-Nishida energy method based on a decomposition of solutions associated with a spectral property of the linearized operator.

Original languageEnglish
Pages (from-to)3248-3295
Number of pages48
JournalJournal of Differential Equations
Volume251
Issue number11
DOIs
Publication statusPublished - Dec 1 2011

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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