Local strong solution to the compressible magnetohydrodynamic flow with large data
Analysis of PDEs
2011-08-30 v1
Abstract
The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local in time strong solution with large initial data is established. The strong solution has weaker regularity than the classical solution. A generalized Lax-Milgram theorem and a Schauder-Tychonoff-type fixed point argument are applied with novel techniques and estimates for the strong solution.
Cite
@article{arxiv.1108.5476,
title = {Local strong solution to the compressible magnetohydrodynamic flow with large data},
author = {Xiaoli Li and Ning Su and Dehua Wang},
journal= {arXiv preprint arXiv:1108.5476},
year = {2011}
}