%0 Journal Article
%T 含有混合耗散的复Ginzburg-Landau方程弱解的适定性和无粘极限<br>Well-Posedness and Inviscid Limit of Weak Solutions to CGL Equation with Mixed Dissipation Terms
%A 郭甜甜
%J Advances in Applied Mathematics
%P 244-261
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/AAM.2025.145253
%X 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L<sup>2</sup>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。<br>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 L<sup>2</sup> 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.
%K 复Ginzburg-Landau方程，截断函数，非线性Schro¨dinger方程，适定性，无粘极限
%K Complex Ginzburg-Landau Equation
%K Truncation Function
%K Nonlinear Schro¨dinger Equation
%K Well-Posedness
%K Inviscid Limit
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115311