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

作者：Zhang Ting; Fang Daoyuan^*

来源：Journal de Mathematiques Pures et Appliquees, 2008, 90(5): 413-449.

DOI：10.1016/j.matpur.2008.06.008

• Anisotropic Navier-Stokes equations
• Cauchy problem
• Global wellposedness

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-p(-1+2/p,1/2) and B-p(-1+2/p,1/2) (T), p >= 2. 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-p(-1+2/p,1/2) norm. In particular, our results imply the global wellposedness of (ANS) with high oscillatory initial data.

• 出版日期2008-11
• 单位浙江大学