Well-posedness of fractional Ginzburg–Landau equation in Sobolev spaces

Abstract

This article is concerned with real fractional Ginzburg–Landau equation. Existence and uniqueness of local and global mild solution for both whole space case and flat torus case are obtained by contraction semigroup method, and Gevrey regularity of mild solution for flat torus case is discussed.

Keywords:

• fractional Ginzburg–Landau equation
• well-posedness
• Sobolev space
• Gevrey regularity

AMS Subject Classifications::

• 35Q99
• 35D10
• 78A99

Acknowledgements

This article is supported by the National Science Foundation of China (Nos 10926141 and 11026156).