Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces - Haspot, Boris (Science China. Mathematics, 2012)
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.