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arXiv · 1408.6025

Entropy dissipation estimates for the Landau equation in the Coulomb case and applications

Laurent Desvillettes
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Abstract

We present in this paper an estimate which bounds from below the entropy dissipation D(f) of the Landau operator with Coulomb interaction by a weighted H^1 norm of the square root of f. As a consequence, we get a weighted L^1_t(L^3_v) estimate for the solutions of the spatially homogeneous Landau equation with Coulomb interaction, and the propagation of L^1 moments of any order for this equation. We also present an application of our estimate to the Landau equation with (moderately) soft potentials, providing thus a new proof of some recent results of Kung-Chien Wu

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Laurent Desvillettes. 2014-08-26. Entropy dissipation estimates for the Landau equation in the Coulomb case and applications. https://arxiv.org/abs/1408.6025

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