Abstract:

This paper mainly studies the global inviscid limit of the Ginzburg-Landau system while the initial data is taken in $L^2(\mathbb{R}^n){\times}L^2(\mathbb{R}^n)\operatorname{or}H^1(\mathbb{R}^n){\times}H^1(\mathbb{R}^n).$ Specifically, we investigate the difference between the solution of the Ginzburg-Landau system and the nonlinear Schrödinger system, and use energy estimate to deal with the difference．It is obtained that the inviscid limit of the solution of the Ginzburg-Landau system is the solution of the nonlinear Schrödinger system．

Key words: Ginzburg-Landau system, inviscid limit, energy estimate, Schr?dinger system