On the global well-posedness for the compressible Navier-Stokes equations with slip boundary condition

Yoshihiro Shibata, Miho Murata

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, we prove a global in time unique existence theorem for the compressible viscous fluids in a bounded domain with slip boundary condition in the maximal Lp-Lq regularity class with 2<p<∞ and N<q<∞ under the assumption that initial data are small enough and orthogonal to rigid motions if domain is rotationally symmetric. To prove the global well-posedness, we use the prolongation argument based on the maximal Lp-Lq regularity estimate of exponentially decay type. The same problem was first treated by Kobayashi and Zajaczkowski [5] in the L2 framework by using the energy method; our approach is completely different from Kobayashi and Zajaczkowski [5].

Original languageEnglish
Pages (from-to)5761-5795
Number of pages35
JournalJournal of Differential Equations
Volume260
Issue number7
DOIs
Publication statusPublished - 2016 Apr 5

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On the global well-posedness for the compressible Navier-Stokes equations with slip boundary condition'. Together they form a unique fingerprint.

  • Cite this