Finite-time blowup for the IPM equation with a uniformly space-time smooth force

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Finite-time blowup for the IPM equation with a uniformly space-time smooth force evidence for this event

This event attributed to Tristan Buckmaster

This event attributed to Codex with GPT-5.6 Sol

This event attributed to Claude

Yes. Theorem 2.1: there are a smooth odd initial density $\rho_{in}\in C^\infty(\mathbb T^2)$ of zero spatial mean, an odd force $F\in C^\infty([0,1]\times\mathbb T^2)$, and a solution smooth on $[0,T]$ for every $T<1$ with $\rho(t)\to\rho_*$ in $C^\eta$ for every $0\le\eta<1$, yet $\|\nabla\rho(t)\|_\infty$ and $\|D_xu_{\mathbb T}(\rho(t))\|_\infty$ both diverging as $t\uparrow1$. The advance over Córdoba and Martínez-Zoroa is precisely the force class, from $L^\infty_t C^\infty_x$ to uniformly space-time smooth, on the torus rather than the plane. Not the Clay Millennium problem: that problem is Navier-Stokes with viscosity, and Fefferman's official description states that the Euler equation "is not on the Clay Institute's list of prize problems". parent of this event

Buckmaster's public statement on the work and its release evidence for this event

Córdoba and Martínez-Zoroa: the theorem extended, and Remark 1's open case evidence for this event

VibeMathed record: Finite-time blowup for the IPM equation with a uniformly space-time smooth force evidence for this event

Finite-time blowup for the IPM equation with a uniformly space-time smooth force parent of this event

This event attributed to Matei P. Coiculescu

This event attributed to Levent Alpöge