Global well-posedness for the 3D incompressible inhomogeneous Navier-Stokes equations and MHD equations

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• 作者：Xiaoping Zhai^a ; ^{pingxiaozhai@163.com} ; Zhaoyang Yin^a ; ^b ; ^{mcsyzy@mail.sysu.edu.cn}
• 关键词：35Q35 ; 35Q30 ; 76D03
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1359-1412
• 全文大小：613 K
• 卷排序：262

文摘

The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier–Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2], and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L2L2 in R3R3. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.