In this talk we shall introduce some nonlinear partial differential systems involving curl, including the quasilinear Maxwell system and Maxwell-Stokes system.
We shall explain the physical background and mathematical difficulties of these systems, and present some recent results on solvability and regularity of the solutions of some boundary value problems. We shall see that existence of solutions of these systems depends on the natural of nonlinearity of the equations, the type of the boundary conditions, and the topology of the domains. Some open problems will also be presented.
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