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Variational and operator methods for Maxwell-Stokes system

  • * Corresponding author: Xing-Bin Pan

    * Corresponding author: Xing-Bin Pan

Dedicated to Professor Wei-Ming Ni on the occasion of his 70th birthday

This work was partially supported by the National Natural Science Foundation of China grant no. 11671143, and 11431005

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  • In this paper we revisit the nonlinear Maxwell system and Maxwell-Stokes system. One of the main feature of these systems is that existence of solutions depends not only on the natural of nonlinearity of the equations, but also on the type of the boundary conditions and the topology of the domain. We review and improve our recent results on existence of solutions by using the variational methods together with modified De Rham lemmas, and the operator methods. Regularity results by the reduction method are also discussed and improved.

    Mathematics Subject Classification: Primary: 35Q61; Secondary: 35A15, 35J20, 35J47, 35J50, 35J57, 35J61, 35J62, 35Q60, 47J30, 78A25.

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