Global well-posedness for the homogeneous Landau equation
Abstract
Global well-posedness and exponential decay to equilibrium are proved for the homogeneous Landau equation from kinetic theory. The initial distribution is only assumed to be bounded and decaying sufficiently fast at infinity. In particular, discontinuous initial configurations that might be far from equilibrium are covered. Despite the lack of a comparison principle for the equation, the proof of existence relies on barrier arguments and parabolic regularity theory. Uniqueness and decay to equilibrium are then obtained through weighted integral inequalities. Although the focus is on the spatially homogeneous case with Coulomb potential, the methods introduced here may be applied elsewhere in nonlinear kinetic theory.
Keywords
Cite
@article{arxiv.1305.2257,
title = {Global well-posedness for the homogeneous Landau equation},
author = {Maria Gualdani and Nestor Guillen},
journal= {arXiv preprint arXiv:1305.2257},
year = {2014}
}
Comments
This paper has been withdrawn due to a crucial computational error in Prop. 2.1. Under the correct bound, the assumptions for a key barrier argument (Lemma 2.4) are hard to verify and might not hold with the generality needed. As the authors feel the proposed method is still of some value, a new but partial result (under extra assumptions, including radial symmetry) will be posted soon