Existence of suitable weak solutions of complex Ginzburg–Landau equations and properties of the set of singular points

Abstract

In this paper, we consider the supercritical complex Ginzburg–Landau equation. We discuss the existence of suitable weak solution in Ω, where Ω is a bounded domain in Rn or the whole space. We also discuss the properties of the set of the singular points of the suitable weak solution in Rn, which means that the possible singular points are located in a bounded ball for any given time and there is no singular point on the whole space after limited time.