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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.

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