Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods

Arnold, Anton; Dolbeault, Jean; Schmeiser, Christian; Wöhrer, Tobias

doi:10.1007/978-3-030-82946-9_1

Cited by 5 publications

(1 citation statement)

References 29 publications

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“…In addition, in this setting, one can study consistency with hydrodynamic limits and non-regularising kinetic PDEs with general initial data. The L 2 -framework is general enough to treat a large class of models [16,14,15], and it can provide sharp estimates for some specific models [7,1,3,2,6]. Precise algebraic features of the framework and estimates with respect to the parameters defining the dynamics were studied in [11].…”

Section: Introductionmentioning

confidence: 99%

How to construct decay rates for kinetic Fokker--Planck equations?

Brigati¹,

Stoltz²

2023

Preprint

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This is a preliminary work. An update to a definitive version will follow. We study time averages for the norm of the solution to kinetic Fokker-Planck equations associated with general Hamiltonians. We provide explicit and constructive decay estimates, allowing fat-tail, sub-exponential and (super-)exponential local equilibria, which also include the classic Maxwellian case. The evolution is subject to a transport operator induced by an external space-confining force. The key step in our estimates is a modified Poincaré inequality, obtained via a Lions-Poincaré inequality and an averaging lemma.

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Section: Introductionmentioning

confidence: 99%

How to construct decay rates for kinetic Fokker--Planck equations?

Brigati¹,

Stoltz²

2023

Preprint

View full text Add to dashboard Cite

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$$\mathrm L^2$$ Hypocoercivity Methods for Kinetic Fokker-Planck Equations with Factorised Gibbs States

Bouin,

Dolbeault,

Ziviani

2024

Springer INdAM Series

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Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations

Achleitner,

Arnold,

Mehrmann

2023

J Dyn Diff Equat

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The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniformly in all directions and anisotropic Oseen-type equations with different viscosity directions. The hypocoercivity index is determined (if it exists) and it is shown that similar to the finite dimensional case of ordinary differential equations and differential-algebraic equations it characterizes its decay behavior.

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Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods

Cited by 5 publications

References 29 publications

How to construct decay rates for kinetic Fokker--Planck equations?

How to construct decay rates for kinetic Fokker--Planck equations?

$$\mathrm L^2$$ Hypocoercivity Methods for Kinetic Fokker-Planck Equations with Factorised Gibbs States

Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations

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