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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 independently of time, and then give the local and global existence of strong solutions. Furthermore, we also obtain the convergence of the global strong solution to a stationary state and the nonlinearly stability of its convergence. It is worth noticing that all the assumptions imposed on the initial data are the same as Takeyuki Nagasawa [Japan.J.Appl.Math.(1988)]. Therefore, our work can be regarded as an improvement of the results of Takeyuki.
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 do
We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singularity do to cavitation at the origin.
We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in $mathbb{R}^n.$ We focus on the so-called critical Besov regularity framework. In this setting, it is natural
In this paper, the initial-boundary value problem of the 1D full compressible Navier-Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any $H^1$ initial data. The
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