Well-Posedness and Inviscid Limit of Weak Solutions to CGL Equation with Mixed Dissipation Terms

复Ginzburg-Landau (CGL)方程作为非平衡系统动力学的普适模型, 在量子流体动力学、 超导 理论及Bose-Einstein疑聚体等物理系统中具有重要应用, 适定性与渐近极限是其数学理论研究中 的重要方向。 本文针对具有混合耗散算子的CGL方程展开系统性研究。 通过混合耗散算子的正则 性分析与特定参数比率约束条件的构造, 确立L2解的唯一性, 井借助与耗散参数相关的截断函数及 能量估计方法, 揭示了耗散系数趋于0时, 从CGL方程到高阶非线性Schro¨dinger (NLS)方程的无 粘极限及其收敛速率。The complex Ginzburg-Landau (CGL) equation, as a universal model for non-equilibrium system dynamics, has important applications in physical systems such as quantum fluid dynamics, superconductivity theory, and Bose-Einstein condensates. Well-posedness and asymptotic limit are important directions in the study of mathematical theory. This article conducts a systematic study on the CGL equation with mixed dissipa- tive operators. By analyzing the regularity of the mixed dissipation operators and constructing specific parameter ratio constraints, the uniqueness of the L2 solution is established. With the help of truncation function and energy estimates related to dissipation parameters, the inviscid limit and convergence rate from CGL equation to high-order nonlinear Schro¨dinger (NLS) equation are obtained when the dissipation coefficients approaches to 0.