Inviscid limit for the derivative Ginzburg-Landau equation with small data in higher spatial dimensions

TL;DR

This paper investigates the inviscid limit of the derivative Ginzburg-Landau equation in higher dimensions, proving global well-posedness and convergence to the derivative Schrödinger equation for small initial data.

Contribution

It establishes the global well-posedness and convergence results for the derivative Ginzburg-Landau equation in higher dimensions, extending previous understanding of the inviscid limit.

Findings

Global well-posedness of the derivative Ginzburg-Landau equation in higher dimensions

Convergence of solutions to the derivative Schrödinger equation as viscosity vanishes

Results valid for small initial data in higher spatial dimensions

Abstract

We study the inviscid limit for the Cauchy problem of derivative Ginzburg-Landau equation in higher dimension space n>2. We show that it is global well-posed and its solution will converge to that of derivative Schrodinger equation.