Navier-Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices

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Abstract

The Cauchy problems for Navier-Stokes equations and nonlinear heat equations are studied in modulation spaces Mq, σs (Rn). Though the case of the derivative index s = 0 has been treated in our previous work, the case s ≠ 0 is also treated in this paper. Our aim is to reveal the conditions of s, q and σ of Mq, σs (Rn) for the existence of local and global solutions for initial data u0 ∈ Mq, σs (Rn).

Original languageEnglish
Pages (from-to)1972-2002
Number of pages31
JournalJournal of Differential Equations
Volume248
Issue number8
DOIs
Publication statusPublished - 2010 Apr 15

Keywords

  • Cauchy problems
  • Heat equations
  • Modulation spaces
  • Navier-Stokes equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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