تقرير
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
| العنوان: | 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 |
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| المؤلفون: | Takahashi, Tomoki |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35Q30, 76D05 |
| الوصف: | 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 $(1+|x|)^\alpha(1+|x|-x_1)^\beta$, 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. Comment: 77 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.14584 |
| رقم الأكسشن: | edsarx.2208.14584 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |