斯托克斯算子在有界和外部 $$C^1$$ 域中的残差估计值

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-08-03 DOI:10.1007/s00208-024-02956-z

Jun Geng, Zhongwei Shen

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引用次数: 0

摘要

我们在 $\mathbb {R}^{d}$ 的有界 $C^1$ 域 $\Omega $ 中建立了斯托克斯算子在 $L^q$ 空间中的解析估计。作为一个推论，斯托克斯算子会在$L^q(\Omega ; \mathbb {C}^d)$中生成一个有界的解析半群，适用于任何$1< q< \infty $和$d\ge 2$.我们还研究了外部$C^1$域的情况。

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Resolvent estimates for the Stokes operator in bounded and exterior $$C^1$$ domains

We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $\Omega $ in $\mathbb {R}^{d}$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(\Omega ; \mathbb {C}^d)$ for any $1< q< \infty $ and $d\ge 2$. The case of an exterior $C^1$ domain is also studied.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.