A global existence of classical solutions to the two-dimensional Vlasov-Fokker-Planck and magnetohydrodynamics equations with large initial data

Bingkang Huang; Lan Zhang

doi:10.3934/krm.2019016

Article Contents

2019, Volume 12, Issue 2: 357-396. Doi: 10.3934/krm.2019016

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A global existence of classical solutions to the two-dimensional Vlasov-Fokker-Planck and magnetohydrodynamics equations with large initial data

Bingkang Huang^1, and
Lan Zhang^2, ,

1.
School of Mathematics, Hefei University of Technology, Hefei 230009, China
2.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

* Corresponding author: Lan Zhang
* Corresponding author: Lan Zhang

Received: March 2018

Revised: July 2018

Published: April 2019

This work was supported by a Grant from National Natural Science Foundation of China under Contract 11671309 and "The Fundamental Research Funds for the Central Universities"

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Abstract

We present a two-dimensional coupled system for particles and compressible conducting fluid in an electromagnetic field interactions, which the kinetic Vlasov-Fokker-Planck model for particle part and the isentropic compressible MHD equations for the fluid part, respectively, and these separate systems are coupled with the drag force. For this specific coupled system, a sufficient framework for the global existence of classical solutions with large initial data which may contain vacuum is established.

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Mathematics Subject Classification: 35A09, 35Q30, 35Q35, 35Q83, 76N10.

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