Global existence and long time behavior of the ellipsoidal-Fokker–Planck equation. Issue 9 (4th July 2019)

• Record Type: Journal Article
• Authors: Sun, Jiawei; Jing, Lei
• Is Part Of: Applicable analysis. Volume 98:Issue 9(2019)
• Page Start: 1605
• Page End: 1625
• Publication Date: 2019-07-04
• Subjects: ES-FP equation -- global existence -- long time behaviors; 35A05 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1434154
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The ellipsoidal-Fokker–Planck (ES-FP) model is proposed recently to obtain the correct Prandtl number in the numerical simulation of rarefied gas flows, which also satisfies the same properties as the Boltzmann equation, such as the H-theorem and the conservation laws of the mass, momentum, and energy. In this paper, we consider the Cauchy problem for this ES-FP equation in R 3, and prove the global existence of the unique solution and establish its algebraic time convergence rate to the equilibrium state.