Existence and stability of periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces
- Resource Type
- Working Paper
- Authors
- Guo, Boling; Qin, Guoquan
- Source
- Subject
- Mathematics - Analysis of PDEs
35Q56, 35B10, 35B35
- Language
We prove the existence of time periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces. We consider the cubic Ginzburg-Landau equation with an external force $g$ satisfying the oddness condition $g(-x,t)=-g(x,t)$. The existence of the periodic solution is proved for small time-periodic external force. The stability of the time periodic solution is also considered.
Comment: 22 pages