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Inspired by the numerical evidence of a potential 3D Euler singularity\cite{luo2014potentially,luo2013potentially-2}, we prove finite timesingularity from smooth initial data for the HL model introduced by Hou-Luo in\cite{luo2014potentially,luo2013potentially-2} for the 3D Euler equations withboundary. Our finite time blowup solution for the HL model and the singularsolution considered in \cite{luo2014potentially,luo2013potentially-2} sharesome essential features, including similar blowup exponents, symmetryproperties of the solution, and the sign of the solution. We use a dynamicalrescaling formulation and the strategy proposed in our recent work in\cite{chen2019finite} to establish the nonlinear stability of an approximateself-similar profile. The nonlinear stability enables us to prove that thesolution of the HL model with smooth initial data and finite energy willdevelop a focusing asymptotically self-similar singularity in finite time.Moreover the self-similar profile is unique within a small energy ball and the$C^\gamma$ norm of the density $\theta$ with $\gamma\approx 1/3$ is uniformlybounded up to the singularity time.

Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations