On the regularity of the global attractor for a damped Rosenau equation on R
On the regularity of the global attractor for a damped Rosenau equation on R
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DOI：
10.1080/00036811.2016.1188285
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发表时间：
2017-06
影响因子：
1.1
通讯作者：
Deqin Zhou;Liying Wang;Chunlai Mu
中科院分区：
文献类型：
--
作者：
Deqin Zhou;Liying Wang;Chunlai Mu
在本文中，我们考虑 上阻尼 Rosenau 方程解的渐近行为。我们应用 Riesz-Rellich 准则的变体（其中涉及 Littlewood-Paley 投影算子）来证明阻尼 Rosenau 方程对于任何 都具有全局吸引子。此外，如果与时间无关的源项在 中且初始数据在 中，则全局吸引子包含在 中。我们的结果建立了分数阶 Sobolev 空间中阻尼 Rosenau 方程的全局吸引子正则性，这是本文的一个新内容。
In this paper, we consider the asymptotic behaviour of the solution for a damped Rosenau equation on . We apply a variant of Riesz–Rellich criteria, which involves the Littlewood–Paley projection operators, to prove that the damped Rosenau equation possesses a global attractor in for any . Moreover, the global attractor is contained in , if the time-independent source term is in and the initial data are in . Our results establish the regularity of the global attractor for the damped Rosenau equation in fractional order Sobolev space, which is a new ingredient in this paper.