Archive for Rational Mechanics and Analysis

, Volume 193, Issue 1, pp 21–55

Smoothing Effects for Classical Solutions of the Full Landau Equation


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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Yemin Chen
    • 1
    • 2
  • Laurent Desvillettes
    • 2
  • Lingbing He
    • 2
    • 3
  1. 1.Department of MathematicsBeijing Institute of TechnologyBeijingPeople’s Republic of China
  2. 2.CMLA, ENS Cachan, CNRS, PRES UniverSudCachan CedexFrance
  3. 3.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China