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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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