On the Initial-Value Problem for the Generalized Two-Dimensional Ginzburg]Landau Equation

The Ginzburg]Landau-type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. Most work so far concentrates on Ginzburg]Landau-type equations with one spatial dimension 1D.. In this paper, the authors study a complex generalized Ginzburg]Landau equation with two spatial dimensions 2D.. Sufficient conditions for the existence and uniqueness of global solutions for the initial-value problem of the generalized 2D Ginzburg]Landau equation are obtained. This rigorously establishes the foundation for further investigation of this type of model.