Turbulence and singularity of the Einstein equation with a negative cosmological constant studied from classical turbulence theory
Project/Area Number 
16K13850

Research Category 
GrantinAid for Challenging Exploratory Research

Allocation Type  Multiyear Fund 
Research Field 
Mathematical physics/Fundamental condensed matter physics

Research Institution  Kyoto University 
Principal Investigator 

Project Period (FY) 
20160401 – 20180331

Project Status 
Completed (Fiscal Year 2017)

Budget Amount *help 
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)

Keywords  古典乱流のカスケード / スケーリング則 / 偏微分方程式の爆発解 / 乱流理論 / 重力方程式 
Outline of Final Research Achievements 
It has been known that a certain spherical symmetric Einstein equation with a negative cosmological constant has a turbulent solution by a numerical simulation. The equation has a global conservation law. The turbulent solution successively generates smallscale activities by respecting a specific scaling law. The generation occurring in an accelerated manner is considered to reach the infinitesimally small scale in a finite time. We studied this turbulent solution and its singular behavior with the method of analyzing turbulence of the NavierStokes equations. In particular, we adopted the picture of the energy cascade in the NavierStokes turbulence to the conservative quantity of the turbulent solution. So far we were not able to explain the exponent of the powerlaw scaling law phenomenologicaly. Nevertheless, the cascade picture shed a new light to the smallscale generation mechanism of the turbulent solution.

Report
(3 results)
Research Products
(2 results)