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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 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:
35Q35PDEs in connection with fluid mechanics
35B65Smoothness and regularity of solutions of PDE
76W05Magnetohydrodynamics and electrohydrodynamics
76E25Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
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