Asymptotic stability of a fluid-particles interaction model with external forces

作者：Jiang, Zaihong^*; Geng, Jinbo^*; Li, Li; Zhong, Ning

来源：Journal of Mathematical Physics, 2018, 59(1): 011511.

DOI：10.1063/1.5022028

• NAVIER-STOKES EQUATIONS
• CLASSICAL-SOLUTIONS
• HYDRODYNAMIC LIMIT
• GLOBAL EXISTENCE
• KINETIC-MODEL
• VLASOV
• SYSTEM
• EULER
• REGIME
• WEAK

We consider the Cauchy problem of the Vlasov- Fokker- Planck equation for the dispersed phase coupled to the incompressible Euler equations with external forces deriving from a potential. Global existence and uniqueness of solution are established using classical energy estimate combined with macro- micro decomposition. With external forces, the asymptotic profile is inhomogeneous, and we estimate the decay rate of the solution to the background profile. The decay is optimal in the sense that it equals the decay rate for the corresponding system without forces {See: Carrillo, J. A., Duan, R. J., and Moussa, A. ["Global classical solutions close to equilibrium to the Vlasov-Euler-Fokker-Planck system," Kinet. Relat. Models 4, 227-258 (2011)]}. Published by AIP Publishing.

• 出版日期2018-1
• 单位浙江师范大学; 哈尔滨工业大学