Large time behavior of solutions to the compressible Navier-stokes equation in an infinite layer

Yoshiyuki Kagei

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 ×(0,a)n ≥ 2, under the no slip boundary condition for the velocity. The Lp decay estimates of the solution are established for all 1≤ p≤∞. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the n - 1 dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup.

Original languageEnglish
Pages (from-to)95-124
Number of pages30
JournalHiroshima Mathematical Journal
Volume38
Issue number1
DOIs
Publication statusPublished - Mar 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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