Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 32, Issue 7-9, Pages 1373-1397Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300600910399
Keywords
barotropic viscous fluids; Besov spaces; critical spaces; Littlewood-Paley theory; scaling; well-posedness
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This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N >= 2. We address the question of well-posedness for large data having critical Besov regularity. Our sole additional assumption is that the initial density be bounded away from zero. This improves the analysis of Danchin (2001) where the smallness of rho - (rho) over bar for some positive constant (rho) over bar was needed. Our result relies on a new a priori estimate for a class of parabolic systems with variable coefficients, which is likely to be useful for the investigation of other models in fluid mechanics.
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