In this paper we address the existence, the asymptotic behavior and stability in L and L, 3 2 < p ≤ ∞, for solutions to the steady state 3D Navier-Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier-Stokes equations in L spaces, and we prove the stability of these soluti...

We give two results that indicate that the relaxation time for the flow governed by the Navier-Stokes-Voigt (NSV) model is sinificantly larger than for the Navier-Stokes equations. We first show that for the Green-Taylor vortex decay problem, NSV admits an exact solution which has a significantly larger half life than for true fluid flow. Second, we observe in a channel flow test that NSV provi...

I n the 1820s Claude Louis Marie Henri Navier1 was a professor at the École des Ponts et Chaussées in Paris, which was the Grande École that trained engineers in nineteenthcentury France. At the same time as publishing his famous fluid equations (now known as the Navier-Stokes equations), he designed the first monumental suspension bridge to be built in Paris over the Seine. His bridge develope...

In this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there exists a unique strong solution of the compressible Navier-Stokes equations with general Navier-slip boundary conditions in an interval of time which is uniform...

We show existence of measure attractors for 2-D stochas-tic Navier-Stokes equations with general multiplicative noise. Abstract. We show existence of measure attractors for 2-D sto-chastic Navier-Stokes equations with general multiplicative noise. 1. Introduction This paper is concerned with existence of attractors in connection with stochastic Navier-Stokes equations in dimension 2. For determ...