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

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  • Xing-Bin Pan

    (The Chinese University of Hong Kong (Shenzhen)
    East China Normal University and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai)

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 $$L^2$$ 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.

Suggested Citation

  • Xing-Bin Pan, 2020. "Maxwell–Stokes system with $$L^2$$ L 2 boundary data and Div–Curl system with potential," Partial Differential Equations and Applications, Springer, vol. 1(5), pages 1-56, October.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:5:d:10.1007_s42985-020-00027-x
    DOI: 10.1007/s42985-020-00027-x
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