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

Pré-print du CMLA 2014-01 - version du 25 août 2014

Auteurs : Laurent Desvillettes

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 K. C. Wu.
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