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physics.flu-dyn2021★ 1 cited
The potentially singular behavior of the 3D Navier-Stokes equations
Thomas Y. Hou
Whether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In t…
physics.flu-dyn2013★ 163 cited
Potentially Singular Solutions of the 3D Incompressible Euler Equations
Guo Luo, Thomas Y. Hou
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynami…
physics.flu-dyn2006
Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations
Thomas Y. Hou, Ruo Li
In this paper, we perform a careful numerical study of nearly singular solutions of the 3D incompressible Euler equations with smooth initial data. We consider the interaction of t…