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arXiv · 1512.01638

Landau equation for very soft and Coulomb potentials near Maxwellians

Kleber Carrapatoso·Stéphane Mischler
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Abstract

This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a method to prove stability estimates of its associated semigroup in large functional spaces. We then deduce existence, uniqueness and fast decay of the solutions to the nonlinear equation in a close-to-equilibrium framework. Our result drastically improves the set of initial data compared to the one considered by Guo and Strain who established similar results in [21, 37, 38]. Our functional framework is compatible with the non perturbative frameworks developed by Villani, Desvillettes and co-authors [42, 17, 16, 13], and our main result then makes possible to improve the speed of convergence to the equilibrium established therein.

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Kleber Carrapatoso, Stéphane Mischler. 2015-12-05. Landau equation for very soft and Coulomb potentials near Maxwellians. https://arxiv.org/abs/1512.01638

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