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Chapitre D'ouvrage Année : 2021

Sharpening of decay rates in Fourier based hypocoercivity methods

Résumé

This paper is dealing with two L2 hypocoercivity methods based on Fourier decomposition and mode-by-mode estimates, with applications to rates of convergence or decay in kinetic equations on the torus and on the whole Euclidean space. The main idea is to perturb the standard L2 norm by a twist obtained either by a nonlocal perturbation build upon diffusive macroscopic dynamics, or by a change of the scalar product based on Lyapunov matrix inequalities. We explore various estimates for equations involving a Fokker-Planck and a linear relaxation operator. We review existing results in simple cases and focus on the accuracy of the estimates of the rates. The two methods are compared in the case of the Goldstein-Taylor model in one-dimension.
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Dates et versions

hal-03078698 , version 1 (16-12-2020)
hal-03078698 , version 2 (25-05-2021)

Identifiants

Citer

Anton Arnold, Jean Dolbeault, Christian Schmeiser, Tobias Wöhrer. Sharpening of decay rates in Fourier based hypocoercivity methods. F. Salvarani. Recent Advances in Kinetic Equations and Applications, 48, Springer INdAM Series, inPress, ⟨10.1007/978-3-030-82946-9_1⟩. ⟨hal-03078698v2⟩
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