Global existence and long time behavior of the ellipsoidal-Fokker–Planck equation

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 ${\mathbb{R}}^3$, and prove the global existence of the unique solution and establish its algebraic time convergence rate to the equilibrium state.

KEYWORDS:

• ES-FP equation
• global existence
• long time behaviors

AMS SUBJECT CLASSIFICATIONS:

• 35A05
• 35B40

Acknowledgements

The authors would like to thank their supervisor, Professor Hailiang Li, for the discussion and comments on this problem.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China grant [grant number 11671384], NNFC-RGC grant [grant number 11461161007] and the Beijing New Century Baiqianwan Talent Project.