Global solutions for 2D coupled Burgers-complex-Ginzburg-Landau equations

Abstract

In this article, we study the periodic initial-value problem of the 2D coupled Burgers-complex-Ginzburg-Landau (Burgers-CGL) equations. Applying the Brezis-Gallout inequality which is available in 2D case and establishing some prior estimates, we obtain the existence and uniqueness of a global solution under certain conditions.

Keywords

• Burgers-CGL equation
• prior estimate
• global solution
• Gagliardo-Nirenberg inequality
• Holder inequality