Ginzburg-Landau equations 金兹堡-朗道方程 郭柏灵, 蒋慕蓉, 李用声. Ginzburg-Landau equations Jincibao-Langdao fang cheng Guo Boling, Jiang Murong, Li Yongsheng

Contents Preface Chapter 1 Background of Ginzburg-Landau Equations 1.1 The Benard convection 1.2 The Couette-Taylor flow 1.3 The plane Poiseuille flow 1.4 The turbulent problem in chemical reaction 1.5 Transition from KS equation to Ginzburg-Landau equation 1.6 Ginzburg-Landau models in superconductivity Chapter 2 Global Solutions and Global Attractors for One Dimensional Ginzburg-Landau Equations 2.1 Global solutions and global attractors 2.2 Analysis for traveling wave solutions 2.3 Instability of the quasi-periodic solutions 2.4 Nonlinear stability of the plane waves 2.5 Finite dimensional inertial manifolds 2.6 Exponential attractors 2.7 Structure of the inertial manifolds 2.8 Gevrey regularity 2.9 Determining nodes 2.10 Dynamical system structure and numerical analysis 2.11 Slow periodic solutions 2.12 Stability of traveling wave solutions 2.13 Upper bound estimates of winding numbers 2.14 Discrete attractors and their dimension estimates 2.15 Stability criterion for perturbed cubic-quintic nonlinear Schrodinger equations 2.16 Nonlinear instability of the plane waves Chapter 3 Global Solutions and Asymptotic Behavior for Higher Dimensional Ginzburg-Landau Equations 3.1 Global solutions 3.2 Cauchy problem in local spaces 3.3 Global attractors for 2D case 3.4 The dynamical length 3.5 Hausdor measures of level sets of solutions 3.6 Global attractors for 2D derivative Ginzburg-Landau equation 3.7 Gevrey regularity and approximate inertial manifolds 3.8 Global attractors for the case of unbounded domain 3.9 Time periodic solutions 3.10 Limits to nonlinear Schr.odinger equations 3.11 Existence of almost periodic solutions Chapter 4 Ginzburg-Landau Equations in Superconductivity 4.1 Cauchy problem 4.2 Global attractors 4.3 Hyperbolic Ginzburg-Landau Equations 4.4 Instability of symmetric vortices Chapter 5 Ginzburg-Landau Model Equations 5.1 The case of deg(g,*Ω)=0 5.2 The case of deg(g,*Ω)≠0 5.3 Equations of Ginzburg-Landau heat flows 5.4 Ginzburg-Landau equations and mean curvature flows References