Finite time blow up for a model of incompressible Navier-Stokes Equations

2018/11/23 by Zhentao Jin, Yi Zhou, Jin, Zhentao +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.09394

openalex publication_date 2018/11/23 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

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.

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