GLOBAL SOLUTIONS TO 2-D INHOMOGENEOUS NAVIER-STOKES SYSTEM WITH GENERAL VELOCITY
Language
en
Article de revue
This item was published in
Journal de Mathématiques Pures et Appliquées. 2013, vol. 100, n° 6, p. 806-831
Elsevier
English Abstract
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations (1.1) with variable viscosity, in a critical functional frame- work which is invariant by the ...Read more >
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations (1.1) with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques in [10] to prove the global existence of solutions to (1.1) with piecewise constant initial density which has small jump at the interface and is away from vacuum. In particular, this latter result removes the smallness condition for the initial velocity in a corresponding theorem of [10].Read less <
English Keywords
Inhomogeneous Navier-Stokes Equations
Littlewood-Paley Theory
Wellposedness
Origin
Hal imported