Ginzburg-Landau超流模型的全局和指数吸引子
Global and exponential attractors for a Ginzburg-Landau model of superfluidity
摘要：
研究了超流性非等温模型解的长时间行为。该模型通过一个非线性微分系统描述了液态~ 4 He中正常相和超流相之间的转变，其中超流相的浓度满足一个非等温的Ginzburg-Landau方程。这个系统，这原来是一致的，其适定性最近已被证明，已被证明是承认的李雅普诺夫功能。这允许证明存在的全局吸引子，其中包括不稳定的固定解决方案的流形。最后，利用半群理论的最新技巧，我们证明了包含全局吸引子的有限分维指数吸引子的存在性。
英文摘要：
The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4He by means of a non-linear differential system, where the concentration of the superfluid phase satisfies a non-isothermal Ginzburg-Landau equation. This system, which turns out to be consistent with thermodynamical principles and whose well-posedness has been recently proved, has been shown to admit a Lyapunov functional. This allows to prove existence of the global attractor which consists of the unstable manifold of the stationary solutions. Finally, by exploiting recent techniques of semigroups theory, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.
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