A study on the global regularity for a model of the 3D axisymmetric Navier-Stokes equations |
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Authors: | Lizheng Tao Jiahong Wu |
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Institution: | Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, USA |
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Abstract: | This paper investigates the global regularity issue concerning a model equation proposed by Hou and Lei (2008) 9] to understand the stabilizing effects of the nonlinear terms in the 3D axisymmetric Navier-Stokes and Euler equations. We establish the global regularity of a generalized version of their model with a fractional Laplacian when the fractional power satisfies an explicit condition. This condition is exactly the same as in the case of the 3D generalized Navier-Stokes equations and is due to the balance between a more regular nonlinearity and a less effective (five-dimensional) Laplacian. |
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Keywords: | 35Q53 35B35 35B65 76D03 |
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