CONVERGENCE RATE FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH EXTERNAL FORCE

DOI Web Site 2 Citations
  • SEIJI UKAI
    Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
  • TONG YANG
    Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
  • HUIJIANG ZHAO
    School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

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<jats:p> For the compressible Navier–Stokes equations with a stationary potential force, the stability of the stationary solutions was studied by Matsumura and Nishida. The convergence rate to the stationary solutions in time was later studied by Deckelnick which was improved by Shibata and Tanaka for more general external forces. This paper deals with the case for the stationary potential force under some smallness condition, to establish an almost optimal convergence rate in L<jats:sup>2</jats:sup>(ℝ<jats:sup>N</jats:sup>)-norm for N ≥ 3. </jats:p>

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