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首页> 外文期刊>Annales scientifiques de l'Ecole normale superieure >STOKES RESOLVENT ESTIMATES IN SPACES OF BOUNDED FUNCTIONS
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STOKES RESOLVENT ESTIMATES IN SPACES OF BOUNDED FUNCTIONS

机译：有界函数空间中的Stokes解析估计

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摘要

The Stokes equation on a domain Omega subset of R-n is well understood in the L-P-setting for a large class of domains including bounded and exterior domains with smooth boundaries provided 1 < p < infinity. The situation is very different for the case p = infinity since in this case the Helmholtz projection does not act as a bounded operator anymore. Nevertheless it was recently proved by the first and the second author of this paper by a contradiction argument that the Stokes operator generates an analytic semigroup on spaces of bounded functions for a large class of domains. This paper presents a new approach as well as new a priori L-infinity-type estimates to the Stokes equation. They imply in particular that the Stokes operator generates a C-0-analytic semigroup of angle pi/2 on C-0,C-sigma (Omega), or a non-C-0-analytic semigroup on L-sigma(infinity)(Omega) for a large class of domains. The approach presented is inspired by the so called Masuda-Stewart technique for elliptic operators. It is shown furthermore that the method presented applies also to different types of boundary conditions as, e.g., Robin boundary conditions.
机译：在L-P设置中，对于一大类域（包括带平滑边界的有界和外部域，提供1 <无穷大）的R-n域的Omega子集上的Stokes方程是众所周知的。对于p =无穷大的情况，情况非常不同，因为在这种情况下，亥姆霍兹投影不再充当有界算子。尽管如此，最近由第一和第二作者通过一个矛盾的论证证明，斯托克斯算子在一类大域的有界函数空间上生成了一个解析半群。本文为Stokes方程提供了一种新方法以及新的先验L-无穷大估计。他们特别暗示Stokes算子在C-0，C-sigma（Omega）上生成一个pi / 2角的C-0分析半群，或者在L-sigma（无穷大）上生成一个非C-0分析半群（Omega）适用于一大类域名。所提出的方法是受所谓的椭圆运算符Masuda-Stewart技术启发的。此外还表明，提出的方法也适用于不同类型的边界条件，例如罗宾边界条件。

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