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Fourier Analysis Methods for the Compressible Navier-Stokes Equations

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

In the last three decades, Fourier analysis methods have known a growing importance in the study of linear and nonlinear PDEs. In particular, techniques based on Littlewood-Paley decomposition and paradifferential calculus have proved to be very efficient for investigating evolutionary fluid mechanics equations in the whole space or in the torus. The present survey overviews results based on Fourier analysis and paradifferential calculus, for the compressible Navier-Stokes equations. Focus is on the initial value problem in the case where the fluid domain is \( \mathbb {R}^{d} \) (or the torus \( \mathbb {T}^{d} \)) with d ≥ 2 and on some asymptotic properties of global small solutions.

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Author information

Authors and Affiliations

  1. Université Paris-Est Créteil, LAMA UMR CNRS 8050, France

    Raphaël Danchin

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  1. Raphaël Danchin
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Correspondence to Raphaël Danchin .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan

    Yoshikazu Giga

  2. Université de Toulon IMATH, Toulon, France

    Antonín Novotný

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Danchin, R. (2018). Fourier Analysis Methods for the Compressible Navier-Stokes Equations. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_49

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