2017 Fiscal Year Final Research Report
Turbulence and singularity of the Einstein equation with a negative cosmological constant studied from classical turbulence theory
| Project/Area Number |
16K13850
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2018-03-31
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| 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 |
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| 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.
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| Free Research Field |
流体物理学
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