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Applied Mathematics and Mechanics

, Volume 34, Issue 5, pp 637–656 | Cite as

Optimal convergence rates for three-dimensional turbulent flow equations

  • Dong-fen Bian (边东芬)Email author
  • Bo-ling Guo (郭柏灵)
Article
  • 92 Downloads

Abstract

In this paper, the convergence rates of solutions to the three-dimensional turbulent flow equations are considered. By combining the L p -L q estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H 3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L 2-norm are obtained when the L p -norm of the perturbation is bounded for some \(p \in [1,\tfrac{6} {5}) \).

Key words

turbulent flow equation k-ε model optimal convergence rate energy estimate 

Chinese Library Classification

O175.2 

2010 Mathematics Subject Classification

76W05 76N10 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dong-fen Bian (边东芬)
    • 1
    Email author
  • Bo-ling Guo (郭柏灵)
    • 2
  1. 1.The Graduate School of China Academy of Engineering PhysicsBeijingP. R. China
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingP. R. China

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