Fujita-Kato theorem for the 3-D inhomogeneous Navier-Stokes equations

Dongxiang Chen, Zhifei Zhang, Weiren Zhao

Research output: Contribution to journalArticle

Abstract

In this paper, we prove the global existence and uniqueness of the solution with discontinuous density for the 3-D inhomogeneous Navier-Stokes equations if the initial data (ρ0,u0)∈L(R3)×Hs(R3) with s>1/2 satisfies 0<c0≤ρ0≤C0<+∞, ||u0||H⋙1/2≤ε for some small ε>0 depending only on c0C0. Furthermore, we introduce the dual method to show that if u0∈Lp(R3) for p∈[6/5,2], the velocity satisfies the decay estimate ||∇ku(t) L2≤C(1+t)-k/2-α(p) for t≥1, k=0, 1, with α(p)=3/2(1/p-1/2).

Original languageEnglish (US)
Pages (from-to)738-761
Number of pages24
JournalJournal of Differential Equations
Volume261
Issue number1
DOIs
StatePublished - Jul 5 2016

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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