Semigroup characterization of Besov type Morrey spaces and well-posedness of generalized Navier-Stokes equations

Chin Cheng Lin, Qixiang Yang

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20 Scopus citations

Abstract

The well-posedness of generalized Navier-Stokes equations with initial data in some critical homogeneous Besov spaces and in some critical Q spaces was known. In this paper, we establish a wavelet characterization of Besov type Morrey spaces under the action of semigroup. As an application, we obtain the well-posedness of smooth solution for the generalized Navier-Stokes equations with initial data in some critical homogeneous Besov type Morrey spaces (Bp,pγ1,γ2)n (12<β<1, γ 12=1-2β), 1<p≤2 and np+2β-2<γ2<np or 2<p<∞, and max{np+2β-2,β-1}<γ2<np, with divergence free. These critical homogeneous Besov type Morrey spaces are larger than corresponding classical Besov spaces and cover Q spaces.

Original languageEnglish
Pages (from-to)804-846
Number of pages43
JournalJournal of Differential Equations
Volume254
Issue number2
DOIs
StatePublished - 15 Jan 2013

Keywords

  • Besov type Morrey spaces
  • BMO spaces
  • Navier-Stokes equations
  • Q spaces
  • Wavelets
  • Well-posedness

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