共查询到18条相似文献,搜索用时 78 毫秒
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研究了不可压缩的Navier-Stokes方程弱解的粘性的连续依赖性.首先利用Moser迭代得到当T> 0时,在Ω×(0,T)上速度■的L∞范数估计.其次讨论了对粘度μ的连续依赖性,并给出了精确的估计. 相似文献
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本文证明了, 在临界Besov 空间中, 速度的竖直方向具有大的初始值的三维不可压缩Navier-Stokes 方程的整体解是唯一存在的. 首先, 引进合适的权函数, 用以控制方程中的非线性项; 其次, 充分利用流体的不可压缩性质, 分别估计速度的水平分量和竖直分量以及压力的水平方向梯度和竖直方向梯度; 最后, 通过适当选取权函数的系数, 得到封闭的能量估计, 从而得到方程的整体适定性. 相似文献
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研究了二维空间中非齐次不可压缩Navier-Stokes/Vlasov-Fokker-Planck方程组的渐近分析,此模型用于塑造流体-粒子的相互作用.运用紧性方法得到ρ~ε,u~ε的强收敛,最终得到由关于粒子宏观密度的对流-扩散方程及不可压缩Navier-Stokes方程组成的极限方程组.本文将相关文献的结果推广到非齐次不可压缩的情形. 相似文献
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1引言不可压Navier-Stokes方程作为流体力学的基本方程,其数值计算一直是科学与工程计算关心的问题.本文考虑定常问题: -ε△u (u·▽)u ▽p = f x∈Ω,▽·u=0 x∈Ω, (1) u =0 x∈(?)Ω.这里ε=1/Re是Reynolds数的倒数,u=(u1,u2,…,ud)为待求流速场,p是待求压力场,f=(f1,f2,…,fd)是给定的体力.Ωv(?) Rd(d=2,3)是有界区域,且具有分片Lipschitz连续边界(?)Ω. 相似文献
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针对相关于不可压缩Navier-Stokes方程数值求解的一类3×3块结构的线性方程组,基于线性方程组的等价形式,构造了一个非精确的块因子分解预处理子,在新的特征值等价矩阵形式的基础上,得到了预处理矩阵特征值实部和虚部的上下界估计.数值实验表明,与已有的预处理子相比,所构造的预处理子可以使得GMRES迭代方法对网格尺寸,网格形式以及粘度系数的依赖性都比较弱,且在迭代步数和CPU时间上都占优. 相似文献
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非定常不可压Navier-Stokes方程的高效和稳健的差分格式Ⅱ 总被引:3,自引:3,他引:0
A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on smoothly nonuniform halfstaggered meshes; this stability also holds for this scheme with the pressure correction projection method. However, it is found that the pressure correction projection method may lead to deviation problems in practical simulation of high Re flow;the reason and the cure is given in this paper in terms of differential-algebraic equations. 相似文献
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本文主要考虑三维广义Navier-Stokes方程的衰减率,其分数阶耗散项为Λ2αu.我们证明,如果三维广义Navier-Stokes方程的弱解u(x,t)属于下面正则集▽u∈Lp(0,∞;Bq,∞0(R3)),2α/p+3/q=2α,3/2α
0∈L2(R3)满足:∫s2|w0(rω)|2dω=Cr2αγ-3+o(r2αγ-3)(r→0),10/α-8≤γ≤25/2α-10.则其扰动方程的每个弱解v(x、t)以最优的上下界依代数收敛到u(x,t),C1(1+t)-γ/2≤‖v(t)-u(t)‖L2≤C2... 相似文献
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In this paper a nine-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. The stationary solutions, the existence of attractor and the global stability of the equations are firmly proved. What is more, that the force f acts on the mode ks and k7 respectively produces two systems, which lead to a much richer and varied phenomenon. Numerical simulation is given at last, which shows a stochastic behavior approached through an involved sequence of bifurcations. 相似文献
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In this paper,the global well-posedness of the three-dimensional incompressible Navier-Stokes equations with a linear damping for a class of large initial data slowly varying in two directions are proved by means of a simpler approach. 相似文献
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B. P. Paneah 《Functional Analysis and Its Applications》2003,37(1):46-60
In this paper, some solvability problems for functional equations of the form
are studied. Here I is a finite closed interval in , F is an unknown continuous function,
and
are given continuous maps of I into itself, and
, and
are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators. 相似文献
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A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations. 相似文献
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Xicheng Zhang 《Journal of Mathematical Analysis and Applications》2008,346(1):336-339
In terms of two partial derivatives of any two components of velocity fields, we give a new criterion for the regularity of solutions of the Navier-Stokes equation in R3. More precisely, let u=(u1,u2,u3) be a weak solution in (0,T)×R3. Then u becomes a classical solution if any two functions of ∂1u1, ∂2u2 and ∂3u3 belong to Lθ(0,T;Lr(R3)) provided with , . 相似文献
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Xiao-jing Cai Quan-sen Jiu Chun-yan Xue 《应用数学学报(英文版)》2007,23(4):637-650
In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions. 相似文献