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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2016

Cauchy problem and exponential stability for the inhomogeneous Landau equation

Résumé

This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct solutions in a close-to-equilibrium setting. Finally, we prove a exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay.
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Dates et versions

hal-01143343 , version 1 (17-04-2015)
hal-01143343 , version 2 (21-12-2015)

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Kleber Carrapatoso, Isabelle Tristani, Kung-Chien Wu. Cauchy problem and exponential stability for the inhomogeneous Landau equation. Archive for Rational Mechanics and Analysis, 2016, ⟨10.1007/s00205-015-0963-x⟩. ⟨hal-01143343v2⟩
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