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2017 Fiscal Year Final Research Report

Turbulence and singularity of the Einstein equation with a negative cosmological constant studied from classical turbulence theory

Research Project

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Project/Area Number 16K13850
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionKyoto University

Principal Investigator

Matsumoto Takeshi  京都大学, 理学研究科, 助教 (20346076)

Project Period (FY) 2016-04-01 – 2018-03-31
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
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 small-scale 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 Navier-Stokes equations. In particular, we adopted the picture of the energy cascade in the Navier-Stokes turbulence to the conservative quantity of the turbulent solution. So far we were not able to explain the exponent of the power-law scaling law phenomenologicaly. Nevertheless, the cascade picture shed a new light to the small-scale generation mechanism of the turbulent solution.

Free Research Field

流体物理学

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Published: 2019-03-29  

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