Global existence and attractors for the two-dimensional Burgers-Ginzburg-Landau equations

This paper investigates the periodic initial value problem for the two-dimensional Burgers-Ginzburg-Landau (2D Burgers-GL) equations, which can be derived from the so-called modulated modulation equations (MME) that govern the dynamics of the modulated amplitudes of some periodic critical modes. The well-posedness of the solutions and the global attractors for the 2D Burgers-GL equations are obtained via delicate a priori estimates, the Galerkin method, and operator semigroup method.