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تسجيل مستخدم جديدGlobal wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations
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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 $B^{-1+frac{2}{p},{1/2}}_{p}(T)$, $pgeq2$. 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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