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

[摘要] The existence of a local-in-time unique solution and loss of smoothness of a full Magneto-Hydro-Dynamics (MHD) system are considered for periodic initial data. The result is proven using Fujita-Kato's method in l(1) based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwell'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. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Navier-Stokes equation;Maxwell equations;MHD;Locally well posedness;Loss of smoothness