Local and global well-posedness results for density-dependent incompressible fluids
Haspot, Boris (2011), Local and global well-posedness results for density-dependent incompressible fluids. https://basepub.dauphine.fr/handle/123456789/6994
TypeDocument de travail / Working paper
Karls Ruprecht Universität
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Abstract (EN)This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in R N with N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity and we aim at stating well-posedness in functional spaces as close as possible to the ones imposed in the incompressible Navier-Stokes system by Cannone, Meyer and Planchon in  where u0 ∈ B N p −1 p, ∞ with 1 ≤ p < +∞ . T his im proves the analysis of ,  and  where u0 is considered belonging to B N p −1 p, 1 with 1 ≤ p < 2 N. Our result relies on a new a priori estimate for transport equation introduced by Bahouri, Chemin and Danchin in  when the velocity u is not considered Lipschitz.
Subjects / Keywordsviscosity
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