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Yanyou Qiao

Publications and source records attributed to Yanyou Qiao.

3 recordsLinked to original sources
arXiv2026

There exist blow-ups in the incompressible Navier-Stokes equation

In this paper, we solve the Navier-Stokes equation, one of the seven Millennium Prize Problems suggested by Clay Mathematics Institute(CMI). In our paper, the fluid is confined in a solid sphere. We prove that, for any initial velocity u0, there has been a force vector f , such that there exists no smooth solution (p,u) to the respective Navier-Stokes equation. This result also holds for the Euler equation. The paper was first published in 2021, soon after, Professor PG Lemarié-Rieusset contact me and tell that there is a possible flaw, because u may be non-integrable when it decreases not very fast. Hence, I withdraw the paper. Through carefull consideration of several years, we think we can choose a fluid confined in a solid sphere to fix it. So, we update the paper now.

math.GM↗
arXiv2021

Explicit solutions to the Navier-Stokes equation and the Euler equation

In this paper, we obtain explicit solutions to the Navier-Stokes equation and the Euler equation. For any initial velocity u0 and the force vector f, exact solutions can be explicitly solved as series, where the coefficients are all known functions determined only by u0 and f. Explicit solutions of this paper can help in global regularity studies in the Navier-Stokes equation and the Euler equation. We admit that the convergence of these series still need to be proved before completely solving the existence of the Navier-Stokes equation and the Euler equation.

math.GM↗