Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations

There’s some exciting very recent work by Alpöge and Buckmaster, building upon prior work by Córdoba and Martínez-Zoroa, in the general topic around the infamous global regularity problem for the incompressible three-dimensional Navier-Stokes equations. It is now widely expected that it should be possible to construct smooth initial data and smooth forcing term that would make these equations develop singularities in finite time; and it should even be possible to do without the forcing term. While these authors do not quite achieve these goals yet, they have made enough of a breakthrough that it looks very feasible to complete these goals in the near future. In particular, they have demonstrated such finite time blowup for three simpler model equations: the incompressible porous medium (IPM) equation, the two-dimensional Boussinesq equation, and the three-dimensional incompressible Euler equations. (The first of these equations was already handled by Córdoba and Martínez-Zoroa, but…