共查询到20条相似文献,搜索用时 15 毫秒
1.
Changjiang Zhu 《Communications in Mathematical Physics》2010,293(1):279-299
In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when
the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ
θ
with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis
is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes
equations with the viscosity coefficient μ(ρ) dependent on the density ρ. 相似文献
2.
针对有壁面边界的可压缩流动问题,提出与基于非等距网格的高精度紧致型差分格式相结合的简化隐式迭代时间推进法,建立求解可压缩Navier-Stokes方程的直接数值模拟方法,提高了计算效率.应用该方法,直接数值模拟两种有壁面边界的二维可压缩流动问题,即可压缩平板边界层流动和可压缩槽道流动. 相似文献
3.
The compactness properties of solutions to time-discretization of compressible Navier-Stokes equations are investigated in three dimensions. The existence of generalized solutions is established. 相似文献
4.
In this paper, we study the finite time blow up of smooth solutions to the Compressible Navier-Stokes system when the initial data contain vacuums. We prove that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group (see Definition 2.2). The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin (Comm Pure Appl Math 51:229–240, 1998) by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions. 相似文献
5.
The compressible Navier-Stokes system (CNS) with density-dependent viscosity coefficients is considered in multi-dimension,
the prototype of the system is the viscous Saint-Venat model for the motion of shallow water. A spherically symmetric weak
solution to the free boundary value problem for CNS with stress free boundary condition and arbitrarily large data is shown
to exist globally in time with the free boundary separating fluids and vacuum and propagating at finite speed as particle
path, which is continuous away from the symmetry center. Detailed regularity and Lagrangian structure of this solution have
been obtained. In particular, it is shown that the particle path is uniquely defined starting from any non-vacuum region away
from the symmetry center, along which vacuum states shall not form in any finite time and the initial regularities of the
solution is preserved. Starting from any non-vacuum point at a later-on time, a particle path is also uniquely defined backward
in time, which either reaches at some initial non-vacuum point, or stops at a small middle time and connects continuously
with vacuum. In addition, the free boundary is shown to expand outward at an algebraic rate in time, and the fluid density
decays and tends to zero almost everywhere away from the symmetry center as the time grows up. This finally leads to the formation
of vacuum state almost everywhere as the time goes to infinity. 相似文献
6.
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper.
These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for the
motion of shallow water, from the Navier-Stokes system for incompressible flows with a moving free surface [14]. These compressible
systems are degenerate when vacuum state appears. We study initial-boundary-value problems for such systems for both bounded
spatial domains or periodic domains. The dynamics of weak solutions and vacuum states are investigated rigorously.
First, it is proved that the entropy weak solutions for general large initial data satisfying finite initial entropy exist
globally in time. Next, for more regular initial data, there is a global entropy weak solution which is unique and regular
with well-defined velocity field for short time, and the interface of initial vacuum propagates along the particle path during
this time period. Then, it is shown that for any global entropy weak solution, any (possibly existing) vacuum state must vanish
within finite time. The velocity (even if regular enough and well-defined) blows up in finite time as the vacuum states vanish.
Furthermore, after the vanishing of vacuum states, the global entropy weak solution becomes a strong solution and tends to
the non-vacuum equilibrium state exponentially in time. 相似文献
7.
基于Hermite多项式的C1型单元构造复杂,限制了最小二乘有限元法的应用.引入高阶光滑的非均匀有理B样条作为基函数简化C1型单元构造,提出求解黏性不可压流动Navier-Stokes方程的最小二乘等几何方法.用Newton法或Picard法对Navier-Stokes方程线性化,用线性化偏微分方程的余量定义最小二乘泛函,导出最小二乘变分方程,用NURBS构造高阶光滑的有限维空间来近似速度场和压力场.计算表明:本文方法计算的二维顶盖驱动流数值解能准确描述流动状况,计算的二维通道内圆柱绕流全局质量损失由最小二乘有限元法的6%降为0.018%,该方法可用于Navier-Stokes方程的求解,并且具有较好的质量守恒性. 相似文献
8.
This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles.Specifically the hydrodynamics limit is performed by employing different time and space scalings.The paper shows that,depending on the magnitude of the parameters which define the scaling,the macroscopic quantities(number density,mean velocity and local temperature)are solutions of the acoustic equation,the linear incompressible Euler equation and the incompressible Navier–Stokes equation.The derivation is formally tackled by the recent moment method proposed by[C.Bardos,et al.,J.Stat.Phys.63(1991)323]and the results generalize the analysis performed in[C.Bianca,et al.,Commun.Nonlinear Sci.Numer.Simulat.29(2015)240]. 相似文献
9.
Susan Friedlander Nataša Pavlović Roman Shvydkoy 《Communications in Mathematical Physics》2006,264(2):335-347
It is proved, using a bootstrap argument, that linear instability implies nonlinear instability for the incompressible Navier-Stokes
equations in Lp for all p ∈ (1,∞) and any finite or infinite domain in any dimension n. 相似文献
10.
Kawashima Shuichi Nishibata Shinya Zhu Peicheng 《Communications in Mathematical Physics》2003,240(3):483-500
We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier–Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L2-energy method with the aid of the Poincaré type inequality.The second author's work was supported in part by Grant-in-Aid for Scientific Research (C)(2) 14540200 of the Ministry of Education, Culture, Sports, Science and Technology and the third author's work was supported by JSPS postdoctoral fellowship under P99217. 相似文献
11.
In this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full
compressible Navier-Stokes equation. By introducing a new linear diffusion wave special to this case, we successfully prove
that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which
are not necessarily of zero integral are suitably small, the unique global solution in time to the full compressible Navier-Stokes
equation exists and asymptotically tends toward the corresponding composite wave whose shifts (in space) of two viscous shock
waves are uniquely determined by the initial perturbations. We then apply the idea to study a half space problem for the full
compressible Navier-Stokes equation and obtain a similar result.
Research is supported in part by NSFC Grant No. 10471138, NSFC-NSAF Grant No. 10676037 and 973 project of China, Grant No.
2006CB805902, in part by Japan Society for the Promotion of Science, the Invitation Fellowship for Research in Japan (Short-Term).
Research is supported in part by Grant-in-Aid for Scientific Research (B) 19340037, Japan. 相似文献
12.
求解Navier-Stokes方程组的组合紧致迎风格式 总被引:1,自引:0,他引:1
给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟. 相似文献
13.
14.
A new proof of the diffusion approximation for ordinary differential equations is given. It is based on an asymptotic expansion of the solution of the corresponding Liouville partial differential equations. In contrast to previous results obtained for the suspension under Holderian mappings of subshift of finite type or Fourier analysis techniques, our proof relies only on symbolic dynamics. 相似文献
15.
The local RBFs based collocation methods (LRBFCM) is presented to
solve two-dimensional incompressible Navier-Stokes equations. In avoiding the ill-conditioned
problem, the weight coefficients of linear combination with respect to the
function values and its derivatives can be obtained by solving low-order linear systems
within local supporting domain. Then, we reformulate local matrix in the global and
sparse matrix. The obtained large sparse linear systems can be directly solved instead
of using more complicated iterative method. The numerical experiments have shown
that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes
equations with high accuracy and efficiency. 相似文献
16.
《Journal of Nonlinear Mathematical Physics》2013,20(3-4):301-311
Abstract Lie reduction of the Navier-Stokes equations to systems of partial differential equations in three and two independent variables and to ordinary differential equations is described. 相似文献
17.
We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes
equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1]). 相似文献
18.
In this work, two-level stabilized finite volume formulations for the
2D steady Navier-Stokes equations are considered.
These methods are based
on the local Gauss integration technique and the lowest equal-order
finite element pair. Moreover, the two-level
stabilized finite volume methods involve solving one small Navier-Stokes
problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and
Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite
volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.
These methods we studied provide an
approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order
as the standard stabilized finite volume method, which involve solving one large
nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods
can save a large amount of computational time. 相似文献
19.
G. Seregin 《Communications in Mathematical Physics》2012,312(3):833-845
We show that a necessary condition for T to be a potential blow up time is limt- T ||v(·,t)||L3=¥{limnolimits_{tuparrow T} |v(cdot,t)|_{L_3}=infty}. 相似文献