Archive for Rational Mechanics and Analysis

, Volume 193, Issue 1, pp 21–55

Smoothing Effects for Classical Solutions of the Full Landau Equation

Article

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

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.

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