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

Jishan Fan and Yong Zhou ()
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Jishan Fan: Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
Yong Zhou: Department of Mathematics, Wenzhou University, Wenzhou 325035, China

Mathematics, 2025, vol. 13, issue 11, 1-10

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.

Keywords: Ginzburg–Landau model; well-posedness; Coulomb gauge (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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