Global weak solutions to the Cauchy problem of compressible Navier–Stokes–Vlasov–Fokker–Planck equations | Zendy

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Global weak solutions to the Cauchy problem of compressible Navier–Stokes–Vlasov–Fokker–Planck equations

Author(s) -

Wang Weiwei

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.3499

Subject(s) - fokker–planck equation , vlasov equation , mathematics , cauchy problem , initial value problem , compressibility , convergence (economics) , drag , mathematical analysis , space (punctuation) , physics , partial differential equation , plasma , quantum mechanics , mechanics , linguistics , philosophy , economics , economic growth

A fluid–particles system of the compressible Navier‐Stokes equations and Vlasov‐Fokker‐Planck equation (including the case of Vlasov equation) in three‐dimensional space is considered in this paper. The coupling arises from a drag force exerted by the fluid onto the particles. We study a Cauchy problem with large data, and establish the existence of global weak solutions through an approximation scheme, energy estimates, and weak convergence. Copyright © 2016 John Wiley & Sons, Ltd.

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