Maxwell–Stokes system with $$L^2$$ boundary data and Div–Curl system with potential

Abstract

This paper concerns the boundary value problems of two partial differential systems involving the operator curl and containing an unknown potential, and under boundary conditions with L 2 boundary data. The first one is the Maxwell-Stokes system. We study solvability of both linear and semilinear Maxwell-Stokes systems under either the Dirichlet boundary condition or the natural boundary condition, and examine regularity of the solutions. The second one is the div-curl system with potential, and we derive solvability and regularity under the Dirichlet boundary condition.Keywords Maxwell system Á Maxwell-Stokes system Á Div-curl system Á Div-curl-system with potential Á L 2 boundary data Á Reduction method Á Modified de Rham lemmaThis article is part of the topical collection dedicated to Prof. Dajun Guo for his 85th birthday, edited by Yihong Du, Zhaoli Liu, Xingbin Pan, and Zhitao Zhang.