Inspired by the numerical evidence of a potential 3D Euler singularity by 30] and the recent breakthrough by Elgindi [10] on the singularity formation of the 3D Euler equation without swirl with C 1,α initial data for the velocity, we prove the finite time singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with C 1,α initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup solution for the 3D Euler equations and the singular solution considered in [29,30] share many essential features, including the symmetry properties of the solution, the flow structure, and the sign of the solution in each quadrant, except that we use C 1,α initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in [10]. We also use some strategy proposed in our recent joint work with Huang in [6] and adopt several methods of analysis in [10] to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the solution of the 3D Euler equations or the 2D Boussinesq equations with C 1,α initial data will develop a finite time singularity. Moreover, the velocity field has finite energy before the singularity time.

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