There exist compactly supported, smooth-before-blow-up solutions of the forced 2D Boussinesq equation that blow up in finite time with a uniformly C^{1,alpha} cap L^2 force for every alpha < sqrt(4/3)-1.
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Finite-time singularity via multi-layer degenerate pendula for the 2D Boussinesq equation with uniform $C^{1,\sqrt{\frac{4}{3}}-1-\epsilon}\cap L^2$ force
There exist compactly supported, smooth-before-blow-up solutions of the forced 2D Boussinesq equation that blow up in finite time with a uniformly C^{1,alpha} cap L^2 force for every alpha < sqrt(4/3)-1.