Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data

Slim Ibrahim; Tsuyoshi Yoneda

Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data

Analysis of PDEs 2011-09-29 v1

Authors: Slim Ibrahim , Tsuyoshi Yoneda

Abstract

Existence of local-in-time unique solution and loss of smoothness of full Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The result is proven using Fujita-Kato's method in $\ell^1$ based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwells's equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the damped-wave operator which does not have any smoothing effect.

Keywords

navier-stokes-maxwell equations magnetohydrodynamics local solvability loss of smoothness fujita-kato method periodic initial data

Cite

@article{arxiv.1109.6089,
  title  = {Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data},
  author = {Slim Ibrahim and Tsuyoshi Yoneda},
  journal= {arXiv preprint arXiv:1109.6089},
  year   = {2011}
}

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