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The present paper is concerned with the quasi-neutral and zero-viscosity limits of Navier–Stokes–Poisson equations in the half-space. We consider the Navier-slip boundary condition for velocity and Dirichlet boundary condition for electric potential. By means of asymptotic analysis with multiple scales, we construct an approximate solution of the Navier–Stokes–Poisson equations involving two different kinds of boundary layer, and establish the linear stability of the boundary layer approximations by conormal energy estimate. 相似文献
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In this paper, we are concerned with the rigorous proof of the convergence of the quantum Navier–Stokes-Poisson system to the incompressible Euler equations via the combined quasi-neutral, vanishing damping coefficient and inviscid limits in the three-dimensional torus for general initial data. Furthermore, the convergence rates are obtained. 相似文献
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We study the three-dimensional Cauchy problem of the Poisson–Nernst–Planck–Navier–Stokes equations. We first show that the corresponding stationary system has a unique semi-trivial solution under a general doping profile. Under initial small perturbations around such the semi-trivial stationary solution and small doping profile, we obtain the unique global-in-time solution to the non-stationary system. Moreover, we prove the asymptotic convergence of the solution toward the semi-trivial stationary solution as time tends to infinity. 相似文献
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Fei Jiang Zhong Tan Qiaolian Yan 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(3):355-380
In this paper, we consider the global behavior of weak solutions of Navier–Stokes–Poisson equations in time in a bounded domain–arbitrary
forces. After proving the existence of bounded absorbing sets, we also obtain the conclusion on asymptotic compactness of
global trajectories generated by the Navier–Stokes–Poisson equations of a compressible fluid.
Supported by NSF(No:10531020) of China and the Program of 985 Innovation Engineering on Information in Xiamen University (2004–2007). 相似文献
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Zuoshunhua Shi 《Journal of Differential Equations》2018,264(3):1550-1580
In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension . For , if the external force is axisymmetric, scaling invariant, continuous away from the origin and small enough on the sphere , we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class . Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular () axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in . 相似文献
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Hyunseok Kim 《Annali dell'Universita di Ferrara》2009,55(2):279-287
We study the stationary Navier–Stokes equations in a bounded domain Ω of R
3 with smooth connected boundary. The notion of very weak solutions has been introduced by Marušić-Paloka (Appl. Math. Optim.
41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005) and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) to obtain
solvability results for the Navier–Stokes equations with very irregular data. In this article, we prove a complete solvability
result which unifies those in Marušić-Paloka (Appl. Math. Optim. 41:365–375, 2000), Galdi et al. (Math. Ann. 331:41–74, 2005)
and Kim (Arch. Ration. Mech. Anal. 193:117–152, 2009) by adapting the arguments in Choe and Kim (Preprint) and Kim and Kozono
(Preprint). 相似文献
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《Journal de Mathématiques Pures et Appliquées》1999,78(5):473-503
The Yosida method was introduced in (Quarteroni et al., to appear) for the numerical approximation of the incompressible unsteady Navier–Stokes equations. From the algebraic viewpoint, it can be regarded as an inexact factorization of the matrix arising from the space and time discretization of the problem. However, its differential interpretation resides on an elliptic stabilization of the continuity equation through the Yosida regularization of the Laplacian (see (Brezis, 1983, Ciarlet and Lions, 1991)). The motivation of this method as well as an extensive numerical validation were given in (Quarteroni et al., to appear).In this paper we carry out the analysis of this scheme. In particular, we consider a first-order time advancing unsplit method. In the case of the Stokes problem, we prove unconditional stability and moreover that the splitting error introduced by the Yosida scheme does not affect the overall accuracy of the solution, which remains linear with respect to the time step. Some numerical experiments, for both the Stokes and Navier–Stokes equations, are presented in order to substantiate our theoretical results. 相似文献
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Alice Gorguis 《Applied Mathematics Letters》2012,25(12):2015-2017
In this paper we will demonstrate an affective approach of solving Navier–Stokes equations by using a very reliable transformation method known as the Cole–Hopf transformation, which reduces the problem from nonlinear into a linear differential equation which, in turn, can be solved effectively. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2004,59(4):465-489
In this paper we consider the incompressible Navier–Stokes equations with a density-dependent viscosity in a bounded domain of . We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary for a very general initial data. Moreover, we provide a blow-up criterion for the regularity of the strong solution. For these results, the initial density need not be strictly positive. It may vanish in an open subset of . 相似文献
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The purpose of this work is to study the global-in-time existence of weak solutions of a viscous capillary model of plasma expressed as a so-called Navier–Stokes–Poisson–Korteweg model for large data in three-dimensional space. Using the compactness argument, we prove the existence of global weak solutions in the classical sense to such system with a cold pressure. 相似文献
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ABSTRACT The combining quasineutral and inviscid limit of the Navier–Stokes–Poisson system in the torus 𝕋 d , d ≥ 1 is studied. The convergence of the Navier–Stokes–Poisson system to the incompressible Euler equations is proven for the global weak solution and for the case of general initial data. 相似文献
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We study the partial regularity problem of the incompressible Navier–Stokes equations. A reverse Hölder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to where denotes the standard weak Lebesgue space. 相似文献
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We show the existence of time periodic solutions of the Navier–Stokes equations in bounded domains of
\mathbb R3{\mathbb R^3} with inhomogeneous boundary conditions in the strong and weak sense. In particular, for weak solutions, we deal with more
generalized conditions on the boundary data for Leray’s problem. 相似文献