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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.

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