Global Regularity of the 3D Axi-Symmetric Navier–Stokes Equations with Anisotropic Data
نویسندگان
چکیده
منابع مشابه
Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data
In this paper, we study the 3D axisymmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some Lp norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction bet...
متن کاملGlobal Regularity for a Family of 3d Models of the Axi-symmetric Navier-stokes Equations
We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the or...
متن کاملA study on the global regularity for a model of the 3D axisymmetric NavierStokes equations
We investigates the global regularity issue concerning a model equation proposed by Hou and Lei [3] to understand the stabilizing effects of the nonlinear terms in the 3D axisymmetric Navier-Stokes and Euler equations. Two major results are obtained. The first one establishes the global regularity of a generalized version of their model with a fractional Laplacian when the fractional power sati...
متن کاملDynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl
In this paper, we study the dynamic stability of the 3D axisymmetric NavierStokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An important property of this 1D model is that one can construct from its solutions a family of exact solutions of the 3D Navier-Stokes equations. The nonlinear...
متن کاملStatistical mechanics of the 3D axi-symmetric Euler equations in a Taylor-Couette geometry
Using an analogy with an Ising-like spin model, we define microcanonical measures for the dynamics of three dimensional (3D) axisymmetric turbulent flow in a Taylor-Couette geometry. We compute the relevant physical quantities and argue that axisymmetry induces a large scale organization in turbulent flows. We show that there exists a low energy, low temperature regime, for which the orthoradia...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2008
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300802108057