| Abstract: |
| We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible
Navier-Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. The key technical challenges in the analysis of the mathematical model are the nondissipative nature of the Vlasov-type particle equation and passage to the weak limits in the multilinear coupling terms. This is joint work with Endre Suli (Oxford) and Cesare Tronci (Surrey). |
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