Semi-Group Theory for the Stokes Operator with Navier-Type Boundary Conditions on L p -Spaces
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- 作者：Hind Al Baba ; Chérif Amrouche…
- 刊名：Archive for Rational Mechanics and Analysis
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：223
- 期：2
- 页码：881-940
- 全文大小：
- 刊物类别：Physics and Astronomy
- 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
- 出版者：Springer Berlin Heidelberg
- ISSN：1432-0673
- 卷排序：223
文摘
In this article we consider the Stokes problem with Navier-type boundary conditions on a domain \({\Omega}\), not necessarily simply connected. Since, under these conditions, the Stokes problem has a non trivial kernel, we also study the solutions lying in the orthogonal of that kernel. We prove the analyticity of several semigroups generated by the Stokes operator considered in different functional spaces. We obtain strong, weak and very weak solutions for the time dependent Stokes problem with the Navier-type boundary condition under different hypotheses on the initial data u0 and external force f. Then, we study the fractional and pure imaginary powers of several operators related with our Stokes operators. Using the fractional powers, we prove maximal regularity results for the homogeneous Stokes problem. On the other hand, using the boundedness of the pure imaginary powers, we deduce maximal \({L^{p}-L^{q}}\) regularity for the inhomogeneous Stokes problem.