タカハシ シュウジ TAKAHASHI Shuji
髙橋 秀慈
所属 東京電機大学 理工学部 理工学科 理学系
東京電機大学大学院 理工学研究科 理学専攻
職種 准教授
言語種別 英語
発行・発表の年月 2021
形態種別 学術研究論文
査読 査読あり
標題 A remark on anisotropic decay rate estimates for the Navier-Stokes equations
執筆形態 単著
掲載誌名 Advances in Mathematical Sciences and Applications
掲載区分 国内
巻・号・頁 30(1),209-216
総ページ数 8
著者・共著者 Shuji Takahashi
概要 For the nonstationary incompressible Navier-Stokes equations with anisotropically decaying external forces and zero initial data in ${\bf R}^n\ (n\ge3)$, we continue to consider anisotropic spatial decay rate estimates of the solutions in the so called Serrin's class.
We utilize the weighted equation approach in the Lebesgue space equipped with the mixed norm in this paper again.
But we here multiply two anisotropically growing functions to the equations at the same time.
The double-weighted solutions for the linearized equations are estimated with the weighted and non-weighted external forces.
The estimates for the nonlinear terms are more complicated.
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In case the temporal decay rates of the external forces are grater than $1$, we show the spatial decay rates of the solutions are almost same as those of the external forces in all directions as well as the isotropic decay rate estimates.