共查询到20条相似文献,搜索用时 15 毫秒
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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
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Antonio Russo 《Ricerche di matematica》2011,60(1):151-176
A classical result of Amick (Acta Math 161:71–130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier–Stokes equations in the plane is extended to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a mixed problem of some interest in the applications. 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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V. ?verák 《Journal of Mathematical Sciences》2011,179(1):208-228
A special class of solutions of the n-dimensional steady-state Navier–Stokes equations is considered. Bibliography: 23 titles. 相似文献
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A. S. Mikhailov 《Journal of Mathematical Sciences》2011,178(3):282-291
A class of sufficient conditions for local boundary regularity of suitable weak solutions of nonstationary three-dimensional
Navier–Stokes equations is discussed. The corresponding results are stated in terms of functionals, which are invariant with
respect to the scaling of the Navier–Stokes equations. Bibliography: 27 titles. 相似文献
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Cheng-Jie Liu Ya-Guang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(4):1187-1225
In this paper, we study the asymptotic behavior for the incompressible anisotropic Navier–Stokes equations with the non-slip boundary condition in a half space of ${\mathbb{R}^3}$ when the vertical viscosity goes to zero. Firstly, by multi-scale analysis, we formally deduce an asymptotic expansion of the solution to the problem with respect to the vertical viscosity, which shows that the boundary layer appears in the tangential velocity field and satisfies a nonlinear parabolic–elliptic coupled system. Also from the expansion, it is observed that away from the boundary the solution of the anisotropic Navier–Stokes equations formally converges to a solution of a degenerate incompressible Navier–Stokes equation. Secondly, we study the well-posedness of the problems for the boundary layer equations and then rigorously justify the asymptotic expansion by using the energy method. We obtain the convergence results of the vanishing vertical viscosity limit, that is, the solution to the incompressible anisotropic Navier–Stokes equations tends to the solution to degenerate incompressible Navier–Stokes equations away from the boundary, while near the boundary, it tends to the boundary layer profile, in both the energy space and the L ∞ space. 相似文献
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In this paper we consider the initial boundary value problem of the Navier–Stokes system with various types of boundary conditions. We study the global-in-time existence and uniqueness of a solution of this system. In particular, suppose that the problem is solvable with some given data (the initial velocity and the external body force). We prove that there exists a unique solution for data which are small perturbations of the previous ones. 相似文献
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We consider the problem of evolution of a finite isolated mass of a viscous incompressible liquid with a free surface. We
assume that the initial configuration of the liquid hasn arbitrary shape, the initial free boundary possesses a certain regularity
and the initial velocity satisfies only natural compatibility and regularity conditions (but its smallness is not assumed).
We prove that this problem is well posed, i.e., we construct a local in time solution belonging to some Sobolev–Slobodetskii
spaces. We expect that this result can be helpful for the analysis of more complicated problems, for instance, problems of
magnetohydrodynamics. Bibliography: 9 titles. 相似文献
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Qionglei Chen Changxing Miao Zhifei Zhang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
In this paper, we improve some known uniqueness results of weak solutions for the 3D Navier–Stokes equations. The proof uses the Fourier localization technique and the losing derivative estimates. 相似文献
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A. Mikhailov 《Journal of Mathematical Sciences》2010,166(1):40-52
A class of sufficient conditions for the local boundary regularity of suitable weak solutions of nonstationary three-dimensional
Navier–Stokes equations is discussed. The corresponding results are stated in terms of functionals invariant with respect
to the scaling of Navier–Stokes equations. Bibliography: 26 titles. 相似文献
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This paper is concerned with the investigation of a generalized Navier–Stokes equation for non-Newtonian fluids of Bingham-type (GNSE, for short) involving a multivalued and nonmonotone slip boundary condition formulated by the generalized Clarke subdifferential of a locally Lipschitz superpotential, a no leak boundary condition, and an implicit obstacle inequality. We obtain the weak formulation of (GNSE) which is a generalized quasi-variational–hemivariational inequality. By introducing an Oseen model as an auxiliary (intermediated) problem and employing Kakutani-Ky Fan theorem for multivalued operators as well as the theory of nonsmooth analysis, an existence theorem to (GNSE) is established. 相似文献