Zhentao Jin, Yi Zhou
Published 2018-11-23Version 1
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.
Extrapolation of solvability of the regularity problem in rough domains
$L^p$-solvability of the Poisson-Dirichlet problem and its applications to the regularity problem
The $L^p$ regularity problem for parabolic operators
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