A Periodic Boundary Problem for a Generalized Ginzburg-Landau Equation
by
Charles Bu
Wellesley College/Brown University

The Ginzburg-Landau equation in higher spatial dimensions

ut=(\nu+i\alpha)Ñ2u-(\kappa+i\beta)|u|2qu+\gammau

has been studied as a model for "turbulent" dynamics in nonlinear partial differential equations. When q=1, this equation has been found for a general class of nonlinear evolution problems including several classical problems from hydrodynamics and other fields of physics and chemistry. For example, it can be derived as a wave envelope or amplitude equation governing wave-packet solution in the study of Taylor-Couette flow, Benard convection and plane Poiseuille flow. There is significant difference in behavior of the hard and soft turbulence in the system when we move up from D=1. This change is caused by the background role the nonlinear Schrödinger equation (NLS) which is the dissipationless limit of the complex Ginzburg-Landau equation. The objective of this paper is to extend the global existence to a 2D Ginzburg-Landau equation with additional third order term with spatial derivatives and fifth order term. We will present a sufficient condition for global solution and give an example of blow-up phenomenon.

Date received: January 9, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caav-02.