权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

The Equations for the Motion of Viscous Incompressible Fluids

粘性不可压缩流体的运动方程

基本信息

批准号：
09640202
负责人：
KATO Hisako
金额：
$ 2.3万
依托单位：
Kyushu University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640202/
关键词：
motion of fluids unique salution global solution nonlinear viscosity incompressible fluids velocity gradient non-Newtonian 非線形性非圧縮性

项目摘要

Head investigator Kato has studied the equations for the motion of viscous incompressible fluids.1. For the periodicity problem, she proved the existence of periodic solu- tions for the Navier-Stokes equations under critical smallness assumption on the data (Ref. Kato [13).2. For the initial boundary value problem, she has found modified Navier- Stokes equations, and has proved the existence of global (in time ) strong solutions which satisfy the Navier-Stokes equations in time intervals when the velocity gradient is below a given constant, and satisfy the equations 'called non-Newtonian' in time intervals when the velocity gradient is above the constant (Ref. Kato [2], [3]). Furthermore, she has shown that the solu- tions of the modified Navier-Stokes quations converge to the solutions of the stationary equations as t * *(Ref. Kato [4]).Investigator Nakao has studied mainly on decay and global existence prob- lems for nonlinear wave equations. Concerning the latter he has derived re- sults which depend on precise decay estimates for energy. He has also derived an interesting result on the decay of local energy for the exterior problem. (Ref. Nakao [1]-[6]).Investigator Hyakutake gives confidence regions of the multinormal mean by two-stage procedures and its asymptotic properties (Ref. Hyakutake [1], [2]).

首席研究员加藤研究了粘性不可压缩流体的运动方程。对于周期性问题，她证明了Navier-Stokes方程在临界小假设下周期解的存在性（参考文献Kato [13]）.对于初边值问题，她发现了修正的Navier-Stokes方程，并证明了当速度梯度低于给定常数时，在时间区间内满足Navier-Stokes方程的整体（在时间上）强解的存在性，当速度梯度高于该常数时，在时间区间内满足“称为非牛顿”的方程（参考文献Kato [2]，[3]）。此外，她还证明了修正的Navier-Stokes方程的解收敛于定常方程的解为t * *（参考文献Kato [4]）。Nakao研究员主要研究非线性波动方程的衰减和整体存在问题。关于后者，他得出的结果依赖于能量的精确衰变估计。他还得出了一个有趣的结果衰减当地能源的外部问题。(Ref. Nakao [1]-[6]）。研究者Hyakutake通过两阶段程序给出了多正态均值的置信域及其渐近性质（参考Hyakutake [1]，[2]）。