Revision 1

Accepted · first revision · record

Title: Rigorous unstable self-similar singularities in incompressible fluid models
Plain: Computer searches in 2025 found self-similar blowup solutions that occur only for finely tuned starting flows (unstable singularities) in simpler 2D fluid models. Turning these numerical profiles into proofs is open.
Precise: Wang et al. (arXiv 2509.14185, 2025) computed families of unstable self-similar profiles to high precision for the Cordoba-Cordoba-Fontelos model, the 2D incompressible porous media equation and the 2D Boussinesq equations with boundary. Prove that at least one such profile yields an exact finite-time singularity from smooth data, by a computer-assisted stability estimate on the finite-codimension set of data attracted to it. Answer: a proof for each profile family.
Settled by: A computer-assisted proof of nonlinear stability modulo finitely many unstable directions for one profile of the unforced equations.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: Profiles were computed numerically in 2025; a rigorous stability proof was the stated next step.
Posed since: 2025