Global existence of smooth solutions to three-dimensional turbulent flow equations

2012/03/26 by Dongfen Bian, Boling Guo, Bian, Dongfen +1
Engineering · Mathematics · Physics and Astronomy · #35A01 #35Q35 #76F02 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35A01 #msc:35Q35 #msc:76F02

paper · pdf · doi:10.48550/arxiv.1203.5566

18 pages

openalex publication_date 2012/03/26 · arxiv created 2012/04/09 · arxiv updated 2012/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with the global existence of smooth solutions to the turbulent flow equations for compressible flows in ℝ³. The global well-posedness is proved under the condition that the initial data are close to the standard equilibrium state in H³-framework. The proof relies on energy estimates about velocity, temperature, turbulent kinetic energy and rate of viscous dissipation. We use several new techniques to overcome the difficulties from the product of two functions and higher order norms. This is the first result concerning k-ε model equations.

Citations

• L q -L r estimates for solutions of the nonstationary stokes equations in an exterior domain and the Navier-Stokes initial value problems inL q spaces

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