GLOBAL WELL-POSEDNESS OF 3-D ANISOTROPIC NAVIER-STOKES SYSTEM WITH SMALL UNIDIRECTIONAL DERIVATIVE
Language
en
Article de revue
This item was published in
Archive for Rational Mechanics and Analysis. 2020
Springer Verlag
Date
2020English Abstract
In [15], the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical Navier-Stokes system has a global unique solution. ...Read more >
In [15], the authors proved that as long as the one-directional derivative of the initial velocity is sufficiently small in some scaling invariant spaces, then the classical Navier-Stokes system has a global unique solution. The goal of this paper is to extend this type of result to the 3-D anisotropic Navier-Stokes system (AN S) with only horizontal dissipation. More precisely, given initial data u0 = (u h 0 , u 3 0) ∈ B 0, 1 2 , (AN S) has a unique global solution provided that |D h | −1 ∂3u0 is sufficiently small in the scaling invariant space B 0, 1 2 .Read less <
English Keywords
Anisotropic Navier-Stokes system
well-posedness
Littlewood-Paley theory
Origin
Hal imported