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Smoothing Effects for Classical Solutions of the Full Landau Equation

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Abstract

In this work, we consider the smoothness of the solutions to the full Landau equation. In particular, we prove that any classical solutions (such as the ones obtained by Guo in a “close to equilibrium” setting) become immediately smooth with respect to all variables. This shows that the Landau equation is a nonlinear and nonlocal analog of an hypoelliptic equation.

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Authors and Affiliations

  1. Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, People’s Republic of China

    Yemin Chen

  2. CMLA, ENS Cachan, CNRS, PRES UniverSud, 94235, Cachan Cedex, France

    Yemin Chen, Laurent Desvillettes & Lingbing He

  3. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Lingbing He

Authors
  1. Yemin Chen
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  2. Laurent Desvillettes
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  3. Lingbing He
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Correspondence to Yemin Chen.

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Communicated by P.-L. Lions

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Chen, Y., Desvillettes, L. & He, L. Smoothing Effects for Classical Solutions of the Full Landau Equation. Arch Rational Mech Anal 193, 21–55 (2009). https://doi.org/10.1007/s00205-009-0223-z

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  • DOI: https://doi.org/10.1007/s00205-009-0223-z

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