Vol. 10, No. 2, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Optimal well-posedness for the inhomogeneous incompressible Navier–Stokes system with general viscosity

Cosmin Burtea

Vol. 10 (2017), No. 2, 439–479
Abstract

In this paper we obtain new well-posedness results concerning a linear inhomogeneous Stokes-like system. These results are used to establish local well-posedness in the critical spaces for initial density ρ0 and velocity u0 such that ρ0 ρ p,13p(3), u0 p,13p1(3), p (6 5,4) for the inhomogeneous incompressible Navier–Stokes system with variable viscosity. To the best of our knowledge, regarding the 3-dimensional case, this is the first result in a truly critical framework for which one does not assume any smallness condition on the density.

Keywords
inhomogeneous Navier–Stokes system, critical regularity, Lagrangian coordinates
Mathematical Subject Classification 2010
Primary: 35Q30, 76D05
Milestones
Received: 26 July 2016
Revised: 18 October 2016
Accepted: 28 November 2016
Published: 23 February 2017
Authors
Cosmin Burtea
Université Paris-Est Créteil
LAMA - CNRS UMR 8050
61 Avenue du Général de Gaulle
94010 Créteil
France