Global solutions for a nonlocal Ginzberg-Landau equation and a nonlocal Fokker-Plank equation

Abstract

This work is devoted to the study of a nonlocal Ginzberg-Landau equation by the semigroup method and a nonlocal Fokker-Plank equation by the viscosity vanishing method. For the nonlocal Ginzberg-Landau equation, there exists a unique global solution in the set $C^0({\mathbb{R}}^{+},H_0^{\frac{\alpha }{2}}(D))\cap L_{loc}({\mathbb{R}}^{+},H_0^{\alpha }(D))$, for $\alpha \in (0,2)$. For the nonlocal Fokker-Plank equation, the regularity of the solution is weaker than that of the nonlocal Ginzberg-Landau equation due to the drift term.

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