Uniformly attracting limit sets for the critically dissipative SQG equation
Uniformly attracting limit sets for the critically dissipative SQG equation
复制标题
DOI：
10.1088/0951-7715/29/2/298
复制
发表时间：
2016-02-01
期刊：
影响因子：
1.7
通讯作者：
Vicol, Vlad
中科院分区：
文献类型：
--
作者：
Constantin, Peter;Zelati, Michele Coti;Vicol, Vlad
我们考虑尺度不变空间 H-1(T-2) 上临界表面准地转 (SQG) 半群 S(t) 的全局吸引子。 [15]中表明，该吸引子是有限维的，并且对于任何 delta > 0，它会吸引 H1+delta(T-2) 中的一致有界集，从而留下 H-1(T-2) 中一致吸引的问题。在本文中，我们结合 De Giorgi 迭代和非线性极大值原理的思想证明了 H-1(T-2) 中的均匀吸引力。
We consider the global attractor of the critical surface quasi-geostrophic (SQG) semigroup S(t) on the scale-invariant space H-1(T-2). It was shown in [15] that this attractor is finite dimensional, and that it attracts uniformly bounded sets in H1+delta(T-2) for any delta > 0, leaving open the question of uniform attraction in H-1(T-2). In this paper we prove the uniform attraction in H-1(T-2), by combining ideas from the De Giorgi iteration and nonlinear maximum principles.