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

Inspired by the numerical evidence of a potential 3D Euler singularity [54, 55], we prove finite time from smooth initial data for HL model introduced Hou-Luo in 55] equations with boundary. Our blowup solution and singular considered share some essential features, including similar exponents, symmetry properties solution, sign solution. We use dynamical rescaling formulation strategy proposed our recent work [11] to establish nonlinear stability an approximate self-similar profile. The enables us that energy will develop focusing asymptotically time. Moreover profile is unique within small ball $$C^\gamma $$ norm density $$\theta $$\gamma \approx 1/3$$ uniformly bounded up