Study on half-space problem for non-linear PDE in Fluid Dynamics and its application

流体动力学非线性偏微分方程半空间问题研究及其应用

• 批准号: 21740105
• 负责人: KUBO Takayuki
• 金额: $ 2.58万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740105/
• 关键词: 関数方程式; 流体力学; ナヴィエ・ストークス方程式; 重み付き空間; 外部領域; 摂動半空間; 斉次重み; 半空間; 重み付き評価; レゾルベント評価

In this study, we studied analysis of weighted Lp space of Navier-Stokes equation, which is the basic equation of fluid dynamics. As a result, if the weight function belongs to the Muckenhoupt weight class, we are able to prove the weighted Lp-Lq estimates of Stokes semigroup in exterior domains, half-spaces and perturbed half spaces. Moreover we could also show the unique existence of the solution to the Navier-Stokes equations and its asymptotic behavior in weighted Lp framework.

本文研究了流体力学基本方程Navier-Stokes方程的加权Lp空间分析。结果表明，如果权函数属于Muckenhoupt权类，我们能够证明Stokes半群在外域、半空间和摄动半空间上的加权Lp-Lq估计。此外，我们还证明了Navier-Stokes方程解的唯一存在性及其在加权Lp框架下的渐近性。