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

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

2011-09-28

arxiv.org/abs/1109.6089v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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