Finite time blow up for a model of incompressible Navier-Stokes Equations
Abstract
T. Tao constructed an averaged Navier-Stokes equations which obey an energy identity. Nevertheless, he proved that smooth solutions can blow up in finite time. This demonstrates that any proposed positive solution to the famous regularity problem for the three dimensional incompressible Navier-Stokes equations which does not use the finer structure of the nonlinearity cannot possibly be successful. In this paper, we propose a very simple model of the Navier Stokes equation which also obey the energy identity and establish a similar result of finite-time blow up . The drawback of our result is that we only work in space dimensions n>=5.
Keywords
Cite
@article{arxiv.1811.09394,
title = {Finite time blow up for a model of incompressible Navier-Stokes Equations},
author = {Zhentao Jin and Yi Zhou},
journal= {arXiv preprint arXiv:1811.09394},
year = {2018}
}
Comments
Similar results have been pubished in "Blow-Up for a Semi-linear Advection-Diffusion System with Energy Conservation" in Chinese Annals of Mathematics, Series B, 30(4), 2009, 433-446 by Dapeng Du and Jing Lv. Also in "Singular and regular solutions of a nonlinear parabolic system" in Nonlinearity 16(2003), no.6, 2083-2097 by Petr Plechac and Vladimir Sverak