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

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00692673
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Submitted on : Tuesday, May 1, 2012 - 11:50:08 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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

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