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Article Dans Une Revue Science China Mathematics Année : 2012

A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations

Résumé

Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations. In this survey paper, we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space. We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.

Dates et versions

hal-00692673 , version 1 (01-05-2012)

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Raphaël Danchin. A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations. Science China Mathematics, 2012, 55 (2), pp.245--275. ⟨10.1007/s11425-011-4357-8⟩. ⟨hal-00692673⟩
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