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20022026
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133 citations

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math.AP2015

Fourier analysis methods for the compressible Navier-Stokes equations

Raphaël Danchin

In the last three decades, Fourier analysis methods have known a growing importance in the study of linear and nonlinear PDE's. In particular, techniques based on Littlewood-Paley…

math.AP2015★ 11 cited

Hölder continuity of solutions to hypoelliptic equations with bounded measurable coefficients

Cyril Imbert, Clément Mouhot

We prove that weak solutions to hypoelliptic equations with bounded measurable coefficients are Hölder continuous. The proof relies on classical techniques developed by De Gi…

math.AP2015

Global Well-Posedness Of A Non-Local Burgers Equation: The Periodic Case

Cyril Imbert, Roman Shvydkoy, Francois Vigneron

This paper is concerned with the study of a non-local Burgers equation for positive bounded periodic initial data. The equation reads …

math.AP2015

Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin film equation

Rana Tarhini

In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for 0<α<2. The equation is a generalization of the one arising in the modeling of hydraulic fracture…