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The inviscid limit for density-dependent incompressible fluids. (English) Zbl 1221.35295
This is very a interesting and technical paper, concerning density-dependent (or nonhomogeneous) incompressible fluids, for viscous and inviscid case. The problems are considered in the whole space \(\mathbb{R}^N\) or in the torus \(\mathbb{T}^N\). Some important results for imcompressible Euler and Navier-Stokes equations are generalized for the nonhomogeneous case: local (or global) existence, uniqueness, blow-up criteria, inviscid limit. Main mathematical tools are related with the Littlewod-Paley decomposition, used to introduce the Besov spaces. Classical estimates in Sobolev spaces, paradifferential calculus (introduced by J.-M. Bony), interpolation theory, are used. Some news estimates concerning the elliptic equation (satisfied by the pressure) are given in the last part, involving Sobolev spaces with negative index of regularity.

35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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