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| A FLUID-PARTICLE MODEL WITH ELECTRIC FIELDS NEAR A LOCAL MAXWELLIAN WITH RAREFACTION WAVE |
| Teng Wang,Yi Wang |
| (College of Applied Sciences, Beijing University of Technology, Beijing 100124, PR China;CEMS, HCMS, NCMIS, Academy of Math. and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences,University of Chinese Academy of Sciences, Beijing 100049, PR China) |
| DOI： |
| Abstract: |
| The paper is concerned with time-asymptotic behavior of solution near a local Maxwellian with rarefaction wave to a fluid-particle model described by the Vlasov-Fokker-Planck equation coupled with the compressible and inviscid fluid by Euler-Poisson equations through the relaxation drag frictions, Vlasov forces between the macroscopic and microscopic momentums and the electrostatic potential forces. Precisely, based on a new micro-macro decomposition around the local Maxwellian to the kinetic part of the fluid-particle coupled system, which was first developed in \cite{LWW3}, we show the time-asymptotically nonlinear stability of rarefaction wave to the one-dimensional compressible inviscid Euler equations coupled with both the Vlasov-Fokker-Planck equation and Poisson equation. |
| Key words: fluid-particle model; rarefaction wave; time-asymptotic stability |