## 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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