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arXiv · 0712.2652

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

Ting Zhang·Daoyuan Fang
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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, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. 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 $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.

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Ting Zhang, Daoyuan Fang. 2008-04-18. Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations. https://doi.org/10.1007/s00220-008-0631-1

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