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Local Well-Posedness of Classical Solutions to the Time-Dependent Ginzburg–Landau Model for Superconductivity in R n

Author

Listed:
  • Jishan Fan

    (Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China)

  • Yong Zhou

    (Department of Mathematics, Wenzhou University, Wenzhou 325035, China
    Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China)

Abstract

In this paper, we prove the local well-posedness of classical solutions ( ψ , A , ϕ ) to the n D ( n ≥ 3 ) time-dependent Ginzburg–Landau model in superconductivity with the choice of Coulomb gauge and the main assumptions ψ 0 , A 0 ∈ H s ( R n ) with div A 0 = 0 in R n and s > n 2 . This result can be used in the proof of regularity criterion and global-in-time well-posedness of the strong solution.

Suggested Citation

  • Jishan Fan & Yong Zhou, 2025. "Local Well-Posedness of Classical Solutions to the Time-Dependent Ginzburg–Landau Model for Superconductivity in R n," Mathematics, MDPI, vol. 13(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1697-:d:1661535
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