Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417068 | Journal of Differential Equations | 2016 | 34 Pages |
Abstract
In this paper, we first prove the local well-posedness of the 2-D incompressible Navier-Stokes equations with variable viscosity in critical Besov spaces with negative regularity indices, without smallness assumption on the variation of the density. The key is to prove for pâ(1,4) and aâBËp,12p(R2) that the solution mapping Ha:Fâ¦âÎ to the 2-D elliptic equation div((1+a)âÎ )=divF is bounded on BËp,12pâ1(R2). More precisely, we prove thatââÎ âBËp,12pâ1â¤C(1+âaâBËp,12p)2âFâBËp,12pâ1. The proof of the uniqueness of solution to (1.2) relies on a Lagrangian approach [15-17]. When the viscosity coefficient μ(Ï) is a positive constant, we prove that (1.2) is globally well-posed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Huan Xu, Yongsheng Li, Xiaoping Zhai,