Bounded imaginary powers and H∞-calculus of the Stokes operator in two-dimensional exterior domains
Bounded imaginary powers and H∞-calculus of the Stokes operator in two-dimensional exterior domains
复制标题
二维外域Stokes算子的有界虚幂和H∞-演算
DOI：
10.1007/s00209-005-0824-7
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发表时间：
2005
影响因子：
0.8
通讯作者：
H. Abels
中科院分区：
文献类型：
--
作者：
H. Abels
目前的贡献涉及斯托克斯算子AqonLqσ(Ω)，1<；q<；∞，其中Ω是C2类的ℝ2中的外部域。证明了Aq允许有界H∞-演算。这意味着Aq的有界虚幂的存在，它有几个重要的应用。-到目前为止，这一性质仅对ℝn，n≥3中的外部域已知。-特别地，这表明Aq在Lqσ(Ω上具有极大正则性。为了证明，必须分析解决方案(λ+AQ)−1的|λ|→∞和λ→0。对于大型λ，这是使用基于[3]的结果的近似预解器来完成的，这些结果是通过应用拟微分边值问题的微积分获得的。对于小λ，我们用势的理论方法分析了文[11]中发展的预解的表示。
The present contribution deals with the Stokes operatorAqonLqσ(Ω), 1<q<∞, where Ω is an exterior domain in ℝ2of classC2. It is proved thatAqadmits a boundedH∞-calculus. This implies the existence of bounded imaginary powers ofAq, which has several important applications. – So far this property was only known for exterior domains in ℝn,n≥3. – In particular, this shows thatAqhas maximal regularity onLqσ(Ω). For the proof the resolvent (λ+Aq)−1has to be analyzed for |λ|→∞ andλ→0. For largeλthis is done using an approximate resolvent based on the results of [3], which were obtained by applying the calculus of pseudodifferential boundary value problems. For smallλwe analyze the representation of the resolvent developed in [11] by a potential theoretical method.