Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces

• Verfasst von: Haspot, Boris [VerfasserIn]
• Titel: Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces
• Verf.angabe: Haspot Boris
• E-Jahr: 2012
• Jahr: 08 February 2012
• Umfang: 28 S.
• Fussnoten: Gesehen am 06.09.2018
• Titel Quelle: Enthalten in: Science China / Mathematics
• Ort Quelle: Beijing : Science China Press, 2010
• Jahr Quelle: 2012
• Band/Heft Quelle: 55(2012), 2, Seite 309-336
• ISSN Quelle: 1869-1862
• DOI: doi:10.1007/s11425-012-4360-8
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 158075435X

Abstract

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 result improves N the analysis of Danchin and of the author inasmuch as we may take initial density in Bpp,1 with 1 p < +∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density.