Necessary and sufficient conditions for the existence of global attractors for semigroups and applications
Necessary and sufficient conditions for the existence of global attractors for semigroups and applications
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DOI：
10.1512/iumj.2002.51.2255
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发表时间：
2002
影响因子：
1.1
通讯作者：
Qingfen Ma;S. Wang;C. Zhong
中科院分区：
文献类型：
--
作者：
Qingfen Ma;S. Wang;C. Zhong
首先利用非共紧性的度量，建立了无限维动力系统全局吸引子存在的几个充分必要条件。然后给出了一个证明全局吸引子存在性的新方法。这种新方法/配方的主要优点是只需要用与建立吸收集相同类型的能量估计来验证必要的紧性条件。换句话说，我们不需要在更高正则性的函数空间中得到估计。特别是，当更高的正则性不可用时，这个性质是有用的，正如在非光滑域上的Navier- Stokes方程的例子所证明的那样。
First we establish some necessary and suYcient con- ditions for the existence of the global attractor of an infinite dimensional dynamical system, using the measure of noncom- pactness. Then we give a new method/recipe for proving the existence of the global attractor. The main advantage of this new method/recipe is that one needs only to verify a necessary compactness condition with the same type of energy estimates as those for establishing the absorbing set. In other words, one doesn't need to obtain estimates in function spaces of higher regu- larity. In particular, this property is useful when higher regularity is not available, as demonstrated in the example on the Navier- Stokes equations on nonsmooth domains.