ﻻ يوجد ملخص باللغة العربية
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.
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A unifo
In this paper, we provide rigorous justification of the hydrostatic approximation and the derivation of primitive equations as the small aspect ratio limit of the incompressible three-dimensional Navier-Stokes equations in the anisotropic horizontal
In this paper, we study the decay rates for the global small smooth solutions to 3D anisotropic incompressible Navier-Stokes equations. In particular, we prove that the horizontal components of the velocity field decay like the solutions of 2D classi
In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $dot{H}^{-alpha}(mathbb{R}^{3})$ or $dot{H}^{-alpha}(mathbb{T}^{3})$ with $0<alphaleq 1/2$. This is ac
In three previous papers by the two first authors, classes of initial data to the three dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitr