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

Abstract

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B_p^{-1+\frac{2}{p},1/2}$ and $B_p^{-1+\frac{2}{p},1/2}(T)$, $p\ge 2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B_p^{-1+\frac{2}{p},1/2}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.

39 pages

Cited by in corpus (3)

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