Optimal convergence rates for the three-dimensional turbulent flow equations

2012/04/24 by Dongfen Bian, Boling Guo, Bian, Dongfen +1
Mathematics · #35Q35 #65M12 #76F60 #93D20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1204.5323

openalex publication_date 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with the convergence rate of solutions to the three-dimensional turbulent flow equations. By combining the L^p-L^q estimates 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 H³-framework. More precisely, the optimal convergence rates of the solutions and its first order derivatives in L²-norm are obtained when the L^p-norm of the perturbation is bounded for some p∈[1, 6/5).

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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