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Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas

Cheng, Bin, Suli, Endre and Tronci, Cesare (2017) Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas Proceedings of the London Mathematical Society.

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Abstract

We prove the global-in-time existence of large-data nite-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 rare ed particles of one species; the incompressible Navier{Stokes system for the bulk uid; and a parabolic evolution equation, involving magnetic di usivity, for the magnetic eld. The physical derivation of our model is given. It is also shown that the weak solution, whose existence is established, has nonincreasing total energy, and that it satis es a number of physically relevant properties, including conservation of the total momentum, conservation of the total mass, and nonnegativity of the probability density function for the energetic particles. The proof is based on a one-level approximation scheme, which is carefully devised to avoid increase of the total energy for the sequence of approximating solutions, in conjunction with a weak compactness argument for the sequence of approximating solutions. 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.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Cheng, Binb.cheng@surrey.ac.ukUNSPECIFIED
Suli, EndreUNSPECIFIEDUNSPECIFIED
Tronci, Cesarec.tronci@surrey.ac.ukUNSPECIFIED
Date : 29 June 2017
Identification Number : 10.1112/plms.12053
Copyright Disclaimer : Copyright 2017. This is the accepted version of the following article: Cheng, B., Süli, E. and Tronci, C. (2017), Existence of global weak solutions to a hybrid Vlasov-MHD model for magnetized plasmas. Proc. London Math. Soc.. doi:10.1112/plms.12053, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1112/plms.12053/
Uncontrolled Keywords : Global weak solution, Vlasov equation, magnetohydrodynamics
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 09 May 2017 11:32
Last Modified : 30 Jun 2017 11:19
URI: http://epubs.surrey.ac.uk/id/eprint/814128

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