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

Laurent Desvillettes (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

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.

Mots clés: Landau equation; Landau operator; entropy dissipation; degenerate diffusion; Coulomb interaction

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Desvillettes. Entropy dissipation estimates for the Landau equation in the Coulomb case and applications. 2014. ⟨hal-01058056⟩