The Resolvent Problem and $${{H^{\infty}}}$$ -calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Resolvent Problem and $${{H^{\infty}}}$$ -calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity

Authors:	Reinhard Farwig Ri Myong-Hwan

Institution:	(1) Department of Mathematics, Darmstadt University of Technology, 64289 Darmstadt, Germany;(2) Institute of Mathematics, Academy of Sciences, Pyongyang, DPR Korea

Abstract:	It is proved that the Stokes operator in L^q -space on an infinite cylindrical domain of ${{\mathbb{R}^{n}}}$ , ${{n \geq 3}}$ , with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded ${{H^{\infty}}}$ -calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight cylinder with bounded cross-section ${{\Sigma}}$ is studied in L ^q ${{(\mathbb{R}; L^{r}_{\omega} (\Sigma))}}$ where ${{1 < q,r < \infty}}$ and ${{\omega \, \epsilon \, A_{r}(\mathbb{R}^{n-1})}}$ is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on ${{\mathcal{R}}}$ -boundedness of operator families and on square function estimates involving Muckenhoupt weights.

Keywords:	:" target="_blank">: " target="_blank"> gif" alt=" $${{H^{\infty}}}$$ " target="_blank">" align="middle" border="0"> -calculus Stokes operator Stokes resolvent estimate Stokes semigroup unbounded cylindrical domains Muckenhoupt weights
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