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

The Cauchy problems for Navier–Stokes equations and nonlinear heat equations are studied in modulation spaces M q , σ s ( R n ) . 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...

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Bibliographic Details
Published in:Journal of Differential Equations 2010-04, Vol.248 (8), p.1972-2002
Main Author: Iwabuchi, Tsukasa
Format: Article
Language:English
Subjects:
Cauchy problems
Heat equations
Modulation spaces
Navier–Stokes equations
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Summary:The Cauchy problems for Navier–Stokes equations and nonlinear heat equations are studied in modulation spaces M q , σ s ( R n ) . 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 M q , σ s ( R n ) for the existence of local and global solutions for initial data u 0 ∈ M q , σ s ( R n ) .
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2009.08.013