Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density

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Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids (2010, background): “that we get strong solutions, and we will show that it is just enough to ask a arbitrary small εregularity on the initial density to get uniqueness. 3 In [19], we improve the results of R. Danchin in [12, 16], in the sense that the initial density belongs to larger spaces B N p p,1 with p∈ [1,+∞[. I”
A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical Lp Framework (2010, result): “The following statement is a consequence of the results that have been proved in [7, 11].”
Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity (2009, unknown): “[15] Assume that ρ0− ρ̄ ∈ Ḃ n 2 2,1 and u0 ∈ Ḃ n 2 −1 2,1 with ρ0 bounded away from zero.”
Existence of global weak solutions for 3D degenerate compressible Navier–Stokes equations (2015, background): “[9] R. Danchin, Well-posedness in critical spaces for barotropic viscous fluids with truly not constant density.”