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Global well posedness for the Maxwell-Navier-Stokes system in 2D. (English) Zbl 1192.35133
Summary: We prove global existence of regular solutions to the full MHD system (or more precisely the Maxwell-Navier-Stokes system) in 2D. We also provide an exponential growth estimate for the H s norm of the solution when the time goes to infinity.
MSC:
35Q30Stokes and Navier-Stokes equations
35Q61Maxwell equations
82C31Stochastic methods in time-dependent statistical mechanics
76A05Non-Newtonian fluids
76W05Magnetohydrodynamics and electrohydrodynamics
76M35Stochastic analysis (fluid mechanics)