Local Well-posedness for the Magnetohydrodynamics in the different two liquids case

Elena Frolova; Yoshihiro Shibata

Local Well-posedness for the Magnetohydrodynamics in the different two liquids case

Analysis of PDEs 2020-03-03 v1

Authors: Elena Frolova , Yoshihiro Shibata

Abstract

We prove the local well-posedness for a two phase problem of magnetohydrodynamics with a sharp interface. The solution is obtained in the maximal regularity space: $H^1_p((0, T), L_q) \cap L_p((0, T), H^2_q)$ with $1 < p, q < \infty$ and 2/p + N/q < 1 $, where$ N$ is the space dimension

Keywords

magnetohydrodynamics two phase problem sharp interface local well-posedness maximal regularity free boundary problem

Cite

@article{arxiv.2003.00057,
  title  = {Local Well-posedness for the Magnetohydrodynamics in the different two liquids case},
  author = {Elena Frolova and Yoshihiro Shibata},
  journal= {arXiv preprint arXiv:2003.00057},
  year   = {2020}
}

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