Well-posedness and dynamics for the fractional Ginzburg-Landau equation

作者：Pu Xueke^*; Guo Boling

来源：APPLICABLE ANALYSIS, 2013, 92(2): 318-334.

DOI：10.1080/00036811.2011.614601

• Ginzburg-Landau equation
• fractional Laplacian
• weak solutions
• smooth solutions
• global attractors
• 35Qxx

This article studies the global well-posedness and long-time dynamics for the nonlinear complex GinzburgLandau equation involving fractional Laplacian. The global existence and some uniqueness criterion of weak solutions are given with compactness method. To study the strong solutions with the semigroup method, we generalize some pointwise estimates for the fractional Laplacian to the complex background and study carefully the linear evolution of the equation. Finally, the existence of global attractors is studied.

• 出版日期2013-2-1
• 单位北京应用物理与计算数学研究所; 重庆大学