ﻻ يوجد ملخص باللغة العربية
We study the long-time behavior an extended Navier-Stokes system in $R^2$ where the incompressibility constraint is relaxed. This is one of several reduced models of Grubb and Solonnikov 89 and was revisited recently (Liu, Liu, Pego 07) in bounded domains in order to explain the fast convergence of certain numerical schemes (Johnston, Liu 04). Our first result shows that if the initial divergence of the fluid velocity is mean zero, then the Oseen vortex is globally asymptotically stable. This is the same as the Gallay Wayne 05 result for the standard Navier-Stokes equations. When the initial divergence is not mean zero, we show that the analogue of the Oseen vortex exists and is stable under small perturbations. For completeness, we also prove global well-posedness of the system we study.
In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which the BGK model with density dependent collision frequency is coupled with the inhomogeneous Navier-Stokes equation through drag forces. To the best
In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and above inde
An old problem asks whether bounded mild ancient solutions of the 3 dimensional Navier-Stokes equations are constants. While the full 3 dimensional problem seems out of reach, in the works cite{KNSS, SS09}, the authors expressed their belief that the
In this paper, the global strong axisymmetric solutions for the inhomogeneous incompressible Navier-Stokes system are established in the exterior of a cylinder subject to the Dirichlet boundary conditions. Moreover, the vacuum is allowed in these sol
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A unifo