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首页> 外文期刊>Discrete and continuous dynamical systems >GLOBAL AND EXPONENTIAL ATTRACTORS FOR A GINZBURG-LANDAU MODEL OF SUPERFLUIDITY
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GLOBAL AND EXPONENTIAL ATTRACTORS FOR A GINZBURG-LANDAU MODEL OF SUPERFLUIDITY

机译：GINZBURG-LANDAU超流动模型的全局和指数吸引子

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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 techinques of semigroups theory, we prove the existence of an exponential attractor of finite fractal dimension which contains the global attractor.
机译：研究了非等温模型在超流体中解的长期行为。该模型通过非线性微分系统描述了〜4He液体中正相和超流体相之间的过渡，其中超流体相的浓度满足非等温Ginzburg-Landau方程。事实证明该系统符合热力学原理，并且最近已经证明了其良好的适切性，该系统已被证明具有Lyapunov功能。这可以证明存在由固定解的不稳定流形组成的整体吸引子。最后，通过利用最新的半群理论技术，我们证明了存在一个包含整体吸引子的有限分形维数的指数吸引子的存在。

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