发表机构
Shandong University; Shandong Youth University of Political Science（山东大学; 山东青年政治学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决了Cazenave的能量临界复金兹堡－朗道方程公开问题，构建了系数一致的临界稳定性框架，建立了无粘极限下的系数一致Strichartz估计。
AI 中文摘要
我们研究带有线性阻尼项$Ru$（$R\geq0$）的能量临界复金兹堡－朗道方程。对于$d=3,4$维无阻尼对齐方程，我们统一处理聚焦和散焦情形，证明$H^1\cap C_0$正则性的持续性以及正时间下的光滑性，这尤其解决了Cazenave提出的能量临界情形的公开问题。在$3\le d\le6$维中，我们针对零色散和无粘极限构建了系数一致的临界稳定性框架，该框架适用于聚焦和散焦情形下独立的归一化复系数路径；从自然能量空间$H^1$中的极限数据出发，我们得到了极限解最大寿命的每个紧子区间上的收敛性。仅显式线性系数误差估计需要更高的正则性，极限过程未用到极限解的整体适定性、散射或整体时空界。在无粘极限下，我们建立了系数一致的齐次和延迟Strichartz估计，关键技术要素是临界力迫空间所需的延迟双端点估计。
英文摘要
Motivated by dissipative approximations of the three-dimensional focusing energy-critical nonlinear Schrödinger equation, we study the inviscid and zero-dispersion limits for general energy-critical complex Ginzburg-Landau equations in dimensions $3\le d\le6$. We develop a new framework for these limits that does not require a global theory for the limiting equation. For limiting data in $H^1$, we prove strong convergence in the critical space, in particular in $L_t^\infty H_x^1$, on every compact subinterval of the maximal lifespan of the limiting solution. This includes strong $H^1$ inviscid convergence to the 3D focusing energy-critical NLS without higher regularity of the limiting data. The diffusion and nonlinear coefficients may vary independently, and both focusing and defocusing cases are treated. Both limits use coefficient-uniform critical stability. The inviscid argument uses low-frequency truncation to overcome the derivative loss at $H^1$, whereas uniform parabolic smoothing yields a quantitative $H^1$ estimate in the zero-dispersion limit. Moreover, for the inviscid limit, we prove the required homogeneous Strichartz estimates and obtain the retarded estimates by establishing a uniform retarded double-endpoint bound for the critical forcing space.
Comments30 pages
