Archive for Rational Mechanics and Analysis

, Volume 193, Issue 1, pp 21–55

Smoothing Effects for Classical Solutions of the Full Landau Equation


    • Department of MathematicsBeijing Institute of Technology
    • CMLA, ENS Cachan, CNRS, PRES UniverSud
  • Laurent Desvillettes
    • CMLA, ENS Cachan, CNRS, PRES UniverSud
  • Lingbing He
    • CMLA, ENS Cachan, CNRS, PRES UniverSud
    • Department of Mathematical SciencesTsinghua University

DOI: 10.1007/s00205-009-0223-z

Cite this article as:
Chen, Y., Desvillettes, L. & He, L. Arch Rational Mech Anal (2009) 193: 21. doi:10.1007/s00205-009-0223-z


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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© Springer-Verlag 2009