Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 607028, 11 pages
http://dx.doi.org/10.1155/2014/607028
Research Article

On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation

School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China

Received 10 December 2013; Accepted 15 February 2014; Published 16 April 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Chunyan Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation in any spatial dimension with rough initial data. For , we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces . For , we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in . The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup to overcome the derivative in the nonlinear term.