论文标题
各向异性加权$ l^q $ - $ l^r $估计外部域中Oseen Semigroup的估计
Anisotropically weighted $L^q$-$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier-Stokes flow past a rigid body
论文作者
论文摘要
我们考虑Navier-Stokes的空间行为流过$ \ Mathbb {R}^3 $中的刚体。本文在具有各向异性权重$（1+ | x |）^α（1+| x | -x_1）^β$的Lebesgue空间中进行了分析，当人体的翻译速度与$ x_1 $ -Direction $ x_1 $ -drirection相似时，在流体的渐近结构中自然出现。我们在外部域中的Oseen Semigroup的各向异性加权$ L^Q $ -L^r $估计值。作为这些估计的应用，我们研究了各向异性加权$ l^Q $空间中Navier-Stokes流的稳定性/可达到性，以获得非平稳溶液的时空行为。
We consider the spatial-temporal behavior of the Navier-Stokes flow past a rigid body in $\mathbb{R}^3$. The present paper develops analysis in Lebesgue spaces with anisotropic weights $(1+|x|)^α(1+|x|-x_1)^β$, which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the $x_1$-direction. We derive anisotropically weighted $L^q$-$L^r$ estimates for the Oseen semigroup in exterior domains. As applications of those estimates, we study the stability/attainability of the Navier-Stokes flow in anisotropically weighted $L^q$ spaces to get the spatial-temporal behavior of nonstationary solutions.
