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Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces. (English) Zbl 1229.35182
The paper deals with viscous compressible barotropic fluids in dimension \(N\geq 2\). The space variable belongs to the whole space \(\mathbb{R}^N\) or to the periodic box \(\mathbb{T}_a^N\) with period \(a_i\) in the \(i\)-th direction. Well-posedness is proved for large data having critical Besov regularity. The result relies on a new apriori estimate for the velocity. A new unknown, called effective velocity, is introduced to weaken one of the coupling between the density and the velocity. In particular, for the first time, uniqueness is obtained without any assumption on the gradiend of the density.

MSC:
35Q30 Navier-Stokes equations
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