Related papers: Stability of bounded global solutions for Navier-S…
We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $…
Motivated by Gilbarg-Weinberger's early work on asymptotic properties of steady plane solutions of the Navier-Stokes equations on a neighborhood of infinity \cite{GW1978} , we investigate asymptotic properties of steady plane solutions of…
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence…
The existence of global regular axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder is proved. The main step in the proof is a proof of the Holder continuity of the swirl. This gives a possibility to prove…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…
In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the…
We prove existence and asymptotic stability of the stationary solution for the compressible Navier-Stokes equations for isentropic gas dynamics with a density dependent diffusion in a bounded interval. We present the necessary conditions to…
We prove the existence of small amplitude, time-quasi-periodic solutions (invariant tori) for the incompressible Navier-Stokes equation on the $d$-dimensional torus $\T^d$, with a small, quasi-periodic in time external force. We also show…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier-Stokes equations supplemented with arbitrary large initial velocity $v\_0$ and almost constantdensity $\varrho\_0$, for large volume…
This paper investigates the time asymptotic stability of composite waves formed by two shock waves within the context of one-dimensional relaxed compressible Navier-Stokes equations. We demonstrate that the composite waves consisting of two…
This is the first part of a two paper sequence in which we prove the global-in-x stability of the classical Prandtl boundary layer for the 2D, stationary Navier-Stokes equations. In this part, we provide a construction of an approximate…
We study the existence and stability of non-trivial steady-state solutions to the two-dimensional incompressible Navier-Stokes equations in an annular domain $\Omega = B(0,b) \setminus \overline{B(0,a)}$ with radii $b>a>0$.The outer…
We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…
For the 3D Navier-Stokes-Maxwell problem on the whole space and in the presence of external time-periodic forces, first we study the existence of time-periodic small solutions, and then we prove their asymptotic stability. We use new type…
We investigate the large-time behavior of solutions to an outflow problem of the full compressible Navier-Stokes equations in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
This paper is concerned with the global solvability for the Navier-Stokes equations describing viscous free surface flows of infinite depth in three and higher dimensions. We first prove time weighted estimates of solutions to a linearized…
We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.