Understanding of turbulent phenomena through dissipative weak solutions to fluid equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 26287023
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University
• Principal Investigator: Sakajo Takashi 京都大学, 理学研究科, 教授 (10303603)
• Co-Investigator(Kenkyū-buntansha): 松本 剛 京都大学, 理学研究科, 助教 (20346076) ; 柴山 允瑠 京都大学, 情報学研究科, 准教授 (40467444) ; 前川 泰則 京都大学, 理学研究科, 准教授 (70507954)
• Co-Investigator(Renkei-kenkyūsha): FUJIWARA Hiroshi 京都大学, 大学院情報学研究科, 准教授 (00362583)
• Research Collaborator: GOTODA Takeshi 北海道大学, 電子科学研究所, 博士研究員
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 応用数学 / 流体力学 / 関数方程式論 / 数理物理 / 統計力学 / 乱流理論 / 渦力学

Outline of Final Research Achievements

Non-smooth solutions to differential equations that dissipate conserved quantity anomalously are called dissipative weak solutions. It is said that dissipative weak solutions to incompressible Euler equations play an important role in understanding of turbulent phenomena, but a little is known due to the difficulty of mathematical treatment of Euler equations. In this project, toward the understanding of turbulent phenomena, we consider two hydrodynamic equations, the generalized Constantin-Lax-Majda-DeGregorio equation and point vortex equations associated Euler-Poincare system, and figure out the connection between dissipative weak solutions to those equations and enstrophy cascade turbulence in terms of the theory of dynamical systems.

Free Research Field

応用数学(数理流体力学)