Abstract.
We investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations, and one more derivative is needed for the density. We point out a smoothing effect on the velocity and a L 1-decay on the difference between the density and the constant reference state. The proof lies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.
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Oblatum 9-II-1999 & 6-I-2000¶Published online: 29 March 2000
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Danchin, R. Global existence in critical spaces for compressible Navier-Stokes equations. Invent. math. 141, 579–614 (2000). https://doi.org/10.1007/s002220000078
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DOI: https://doi.org/10.1007/s002220000078