Mathematical analysis of nonlinear partial differential equations related with vorticity fields of viscous incompressible flows

粘性不可压缩流涡量场非线性偏微分方程的数学分析

• 批准号: 20840033
• 负责人: MAEKAWA Yasunori
• 金额: $ 2.07万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (Start-up)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20840033/
• 关键词: 偏微分方程式; 流体力学; 非圧縮性粘性流体; Navier-Stokes方程式; 渦度方程式; Burgers渦; 安定性解析; 非線形偏微分方程式; 渦度場; 自己相似解

It is well-known that vorticity fields play important roles in dynamics of incompressible flows. This research aims to analyze linear and nonlinear partial differential equations related with vorticity fields mathematically. As one of the results obtained in this research, it is rigorously proved that some stationary solutions which are known as a model of a coherent structure of vortex tubes in turbulent flows are asymptotically stable with respect to small three-dimensional perturbation flows. This research has successfully made an important contribution in the theory of partial differential equations and the study of the dynamics of turbulent flows.

众所周知，涡度场在不可压缩流的动力学中起着重要作用。本研究旨在对与涡度场相关的线性和非线性偏微分方程进行数学分析。作为本研究取得的成果之一，严格证明了一些被称为湍流中涡管相干结构模型的稳态解对于三维小扰动流是渐近稳定的。这项研究成功地为偏微分方程理论和湍流动力学研究做出了重要贡献。

项目成果

Stability of the axisymmetric Burgers vortex

轴对称伯格斯涡的稳定性

• 发表时间: 2009
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI;Yasunori Maekawa;安田健彦;Y. MATSUI;前川泰則;Yutaka MATSUI;Takehiko Yasuda;Yasunori Maekawa
• 通讯作者: Yasunori Maekawa

Asymmetric Burgers vortices at large circulation

大循环时的不对称汉堡涡流

• 发表时间: 2008
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI;Yasunori Maekawa;安田健彦;Y. MATSUI;前川泰則;Yutaka MATSUI;Takehiko Yasuda;Yasunori Maekawa;安田健彦;Y.MATSUI;前川泰則;Takehiko Yasuda;Yutaka MATSUI;前川泰則;安田健彦;Yutaka MATSUI;前川泰則;安田健彦;前川泰則;前川泰則;前川泰則;前川泰則;前川泰則;Yasunori Maekawa;前川 泰則;前川 泰則;前川泰則;Fumikazu Nagasato;Yasunori Maekawa
• 通讯作者: Yasunori Maekawa

Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance

存在平移和标度不变性时演化方程解的渐近行为

• DOI: 10.1016/j.jfa.2011.02.004
• 发表时间: 2011
• 期刊: J.Functional Analysis
• 作者: Fang Li;Kimie Nakashima;Koichi Kawakami;Yoshiyuki Kagei
• 通讯作者: Yoshiyuki Kagei

On a free boundary problem of the coupled Navier-Stokes / mean curvature equations

耦合纳维-斯托克斯/平均曲率方程的自由边界问题

• 发表时间: 2008
• 作者: Yutaka MATSUI;Kiyoshi TAKEUCHI;Yasunori Maekawa;安田健彦;Y. MATSUI;前川泰則;Yutaka MATSUI;Takehiko Yasuda;Yasunori Maekawa;安田健彦;Y.MATSUI;前川泰則;Takehiko Yasuda;Yutaka MATSUI;前川泰則;安田健彦;Yutaka MATSUI;前川泰則;安田健彦;前川泰則;前川泰則;前川泰則;前川泰則;前川泰則;Yasunori Maekawa;前川 泰則;前川 泰則;前川泰則;Fumikazu Nagasato;Yasunori Maekawa;Fumikazu Nagasato;Yasunori Maekawa;長郷文和;Yasunori Maekawa
• 通讯作者: Yasunori Maekawa

A lower bound for fundamental solutions of the heat convection equations

热对流方程基本解的下界

• 发表时间: 2008
• 期刊: Archive for Rational Mechanics and Analysis 189no.1
• 作者: Maekawa;Y.
• 通讯作者: Y.