Some A priori estimates for the homogeneous Landau equation with soft potentials

By Radjesvarane Alexandre, Jie Liao, Chunjin Lin. 2013

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This paper deals with the derivation of some \'a priori estimates for the homogeneous Landau equation with soft potentials. Using the coercivity of the Landau operator for soft potentials, we prove a global estimate of weak solutions in $L^2$ space without any smallness assumption on the initial data for $ -2 < \gamma <0$. For the stronger case $ -3 \leq \gamma \leq -2$, which covers in particular the Coulomb case, we get such a global estimate, but in some weighted $L^2$ space and under a smallness assumption on initial data.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/20a02876d8d0cb4e886928e01f5cbcd8fd2ccb75

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In Applied Mathematics

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Citations in the corpus

Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, background): “Finally, we highlight the related results of regularisation for the Boltzmann equation without long-range interactions [19, 15, 16], and the related perturbative results for the Landau and (long-range interaction) Boltzmann equation [40, 38, 4, 5, 2, 62, 3].”
Upper bounds for parabolic equations and the Landau equation (2015, background): “This is a contrast with the previous results in [1] and [14] which show a propagation of estimates.”