Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
复制标题
无界圆柱体中斯托克斯算子指数加权勒贝格空间的最大正则性
DOI：
10.1515/anly-2014-1294
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
R. Farwig
中科院分区：
文献类型：
--
作者：
Myong;R. Farwig
摘要研究了Lq-空间中Stokes算子的预解估计和极大正则性，其中Lq-空间在轴向上具有指数权，且Lq-空间中的Stokes算子是无界圆柱，n ≥ 3。对于一个直的圆柱体，我们在轴向方向上使用指数权重，在横截面上使用Muckenhoupt权重。其次，对于具有多个无穷远出口的圆柱，我们证明了具有指数权的Lq-空间中的Stokes算子生成一个指数衰减的解析半群，并且具有极大正则性。直圆柱的证明使用了算子值傅立叶乘子定理和基于一维部分傅立叶变换的相位变量参数化的圆柱横截面中的系统的解算子族的有界性的无条件Schauder分解。对于一般的圆柱体，我们使用截断技术的基础上的结果，直柱和情况下，没有指数权重。
Abstract We study resolvent estimates and maximal regularity of the Stokes operator in Lq-spaces with exponential weights in the axial directions of unbounded cylinders of ℝn, n ≥ 3. For a straight cylinder we use exponential weights in the axial direction and Muckenhoupt weights in the cross-section. Next, for cylinders with several exits to infinity we prove that the Stokes operator in Lq-spaces with exponential weights generates an exponentially decaying analytic semigroup and has maximal regularity. The proof for straight cylinders uses an operator-valued Fourier multiplier theorem and unconditional Schauder decompositions based on the ℛ-boundedness of the family of solution operators for a system in the cross-section of the cylinder parametrized by the phase variable of the one-dimensional partial Fourier transform. For general cylinders we use cut-off techniques based on the result for straight cylinders and the case without exponential weight.