Global wellposed problem for the 3-D incompressible anisotropic Navier–Stokes equations

✍ Scribed by Ting Zhang; Daoyuan Fang

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 421 KB
• Volume: 90
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2008.06.008

✦ Synopsis

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (ANS).

In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, B

Then, we prove the global wellposedness for (ANS) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than B -1+ 2 p , 1 2 p norm. In particular, our results imply the global wellposedness of (ANS) with high oscillatory initial data.