Fluids, geometry, and the onset of Navier-Stokes turbulence in three space dimensions

PHYSICA D-NONLINEAR PHENOMENA

卷:376

Article

Chen, Gui-Qiang^1,2,3  Slemrod, Marshall⁴  Wang, Dehua⁵ 

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

[2] Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China

[3] Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China

[4] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[5] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

关键词: Incompressible Euler equations;    Compressible Euler equations;    Isometric immersion problem;    Riemann curvature tensor;    Navier-Stokes equations;    Turbulence;   

DOI  :  10.1016/j.physd.2017.08.004

来源: Elsevier

【 摘 要 】

A theory for the evolution of a metric g driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in the six-dimensional Euclidean space. The Nash-Kuiper theorem is then applied to this Riemannian manifold to produce a wild evolving C-1 manifold. The theory is applied to the incompressible Euler and Navier-Stokes equations. One practical outcome of the theory is a computation of critical profile initial data for what may be interpreted as the onset of turbulence for the classical incompressible Navier-Stokes equations. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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