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二维N-S方程的Fourier非线性Galerkin方法*

侯延仁

侯延仁. 二维N-S方程的Fourier非线性Galerkin方法*[J]. 应用数学和力学, 1996, 17(9): 829-836.
引用本文: 侯延仁. 二维N-S方程的Fourier非线性Galerkin方法*[J]. 应用数学和力学, 1996, 17(9): 829-836.
Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.
Citation: Hou Yanren. Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1996, 17(9): 829-836.

二维N-S方程的Fourier非线性Galerkin方法*

基金项目: * 国家攀登计划项目

Fourier Nonlinear Galerkin Approximation for the Two Dimensional Navier-Stokes Equations

  • 摘要: 本文对周期边界条件Navier-Stokes方程,证明了其Fourier非线性Galerkin逼近解的存在唯一性,同时给出了逼近解的误差估计。
  • [1] C.Foias.O.Manley and R.Temam,Modelization of the interaction of small and large eddies in two dimensional turbulent flows,Math.Mod.Numer.Anal.M2AN,22(1988),93-144.
    [2] M.Marion and R.Temam,Nonlinear Galerkin methods,SIAM J.Numer.Anal.,26(1989),1139-1157.
    [3] M.Marion and R.Temam,Nonlinear Galerkin methods:the finite case elements case,Numer.Math.,57(1990),205-255.
    [4] R.Temam,Navier-Stokes Equarions,North-Holland Publishing Company,3rd revised edition(1984).
    [5] R.Teman,Navier-Stokes equations and nonlinear functional analysis,CBMS-NSF Regional Conk:Ser.in Appl.Math.,Society for Industrial and Applied Mathematics.Philadelphia,PA,(1983).
    [6] E.Weinan,Convergence of Fourier methods for the Navier-Stokes equations,SIAM J.Numer.Anal.,2(1993),650-674.
    [7] J.G.Heywood and R.Rannacher,Finite element approximation of the nonstationarv Navier-Stokes problem.I.Regularity of solutions and second-order error estimates for spatial discretization,SIAM J.Numer.Anal.,19(1982).275-311.
    [8] H.Okamoto,On the semi-discrete finite element approximation for the nonstationary Navier-Stokes equation,J,Fac.Sci.,Univ.of Tokyo Sec.IA Math,29(1982).613-652.
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  • 刊出日期:  1996-09-15

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