Existence of attractor for the quasi-geostrophic approximation of the Navier-Stokes equations and estimate of its dimension

Abstract This short note studies the problem of a global expansion of local results on existence of strong and classical solutions of Navier-Stokes equations in R 3..

The main results of this paper are as follows: (i) assuming the uniform Lopatinski condi- tion and transversality of layer profiles (Definitions 1.16 and 1.11), we construct

Lorsqu’un écrit scientifique issu d’une activité de recherche financée au moins pour moitié par des dotations de l’État, des collectivités territoriales ou des

initial and boundary value problem for viscous incompressible nonhomogeneous fluids, J. 2014 An existence theorem for compressible viscous and heat. conducting fluids,

The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method

in Sobolev spaces of sufficiently high order, then we show the existence of a solution in a particular case and finally we solve the general case by using the

NIRENBERG, Partial regularity of suitable weak solutions of the Navier-Stokes equations. FRASCA, Morrey spaces and Hardy-Littlewood maximal

In Section 2, we prove a few orthogonality results concerning the Navier- Stokes equations with profiles as initial data, which will be used in the proof ofTheorem 2.. Section 3