Hypocoercivity of the linearized BGK equation with stochastic coefficients

Herzing, Tobias; Klingenberg, Christian; Pirner, Marlies

Research article (journal) | Peer reviewed

Abstract

We consider an approximation of the Boltzmann equation, the Bathnagar-Gross-Krook (BGK) equation. This equation is used in many applications because it is very efficient in numerical simulations. In this paper we study the effect of randomness on a BGK-model. We prove exponential decay rate to a global equilibrium. In addition we prove the decay rate of the -th derivative with respect to the stochastic variable of the solutions. The novelties are i) for the first time hypocoercivity is shown for a linearized BGK model that conserves mass, momentum and energy with randomness in the collision frequency, ii) new estimates for the decay of the derivatives of the solution with respect to the stochastic variable, which is very useful in applications.

Details about the publication

JournalMethods and Applications of Analysis
Volume30(3)
Page range113-128
StatusPublished
Release year2023
DOI10.4310/MAA.2023.v30.n3.a2
Link to the full texthttps://arxiv.org/abs/2008.00322
KeywordsBGK equation; hypocoercivity; uncertainty quantification

Authors from the University of Münster

Pirner, Marlies
Juniorprofessur für Angewandte Mathematik (Prof. Pirner)