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Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data. (English) Zbl 1248.35161
Summary: 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 ${\ell }^{1}$ 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.
##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions of PDE 76W05 Magnetohydrodynamics and electrohydrodynamics 76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
##### References:
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