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This is Part II of our paper in which we prove finite time blowup of the 2DBoussinesq and 3D axisymmetric Euler equations with smooth initial data offinite energy and boundary. In Part I of our paper [ChenHou2023a], we establishan analytic framework to prove stability of an approximate self-similar blowupprofile by a combination of a weighted $L^\infty$ norm and a weighted $C^{1/2}$norm. Under the assumption that the stability constants, which depend on theapproximate steady state, satisfy certain inequalities stated in our stabilitylemma, we prove stable nearly self-similar blowup of the 2D Boussinesq and 3DEuler equations with smooth initial data and boundary. In Part II of our paper,we provide sharp stability estimates of the linearized operator by constructingspace-time solutions with rigorous error control. We also obtain sharpestimates of the velocity in the regular case using computer assistance. Theseresults enable us to verify that the stability constants obtained in Part I[ChenHou2023a] indeed satisfy the inequalities in our stability lemma. Thiscompletes the analysis of the finite time singularity of the axisymmetric Eulerequations with smooth initial data and boundary.

Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics