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

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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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Authors and Affiliations

  1. LAMA UMR 8050, Université Paris-Est, 61, avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Raphaël Danchin

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  1. Raphaël Danchin
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Correspondence to Raphaël Danchin.

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Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Danchin, R. A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations. Sci. China Math. 55, 245–275 (2012). https://doi.org/10.1007/s11425-011-4357-8

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