Existence of Global Weak Solutions to a Hybrid VlasovMHD Model for Magnetized Plasmas
Cheng, Bin, Suli, Endre and Tronci, Cesare (2017) Existence of Global Weak Solutions to a Hybrid VlasovMHD Model for Magnetized Plasmas Proceedings of the London Mathematical Society, 115 (4). pp. 854896.

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Abstract
We prove the globalintime existence of largedata niteenergy weak solutions to an incompressible hybrid Vlasovmagnetohydrodynamic 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 onelevel 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 Vlasovtype 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 : 


Date :  29 June 2017  
DOI :  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 VlasovMHD 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 :  16 Jan 2019 17:14  
URI:  http://epubs.surrey.ac.uk/id/eprint/814128 
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