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Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity. (English) Zbl 1099.35137

Summary: The time-dependent Ginzburg-Landau equations of superconductivity with a time-dependent magnetic field \(\mathbf{H}\) are discussed. We prove existence and uniqueness of weak and strong solutions with \(H^1\)-initial data. The result is obtained under the “\(\phi =-\omega(\nabla\cdot\mathbf{A})\)” gauge with \(\omega > 0\). These solutions generate a dynamical process and are uniformly bounded in time.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanics of superconductors
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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