Year: 2026
Type: preprint
Abstract: By adapting the techniques used in the IPM blowup result of Córdoba-Martínez-Zoroa with spatially smooth force, we prove finite-time blow-up for the IPM equation on $\mathbb T^2$ with a uniformly spacetime smooth force. In particular, we show there exist a smooth odd initial density, a smooth odd force $F\in C^\infty([0,1]\times\mathbb T^2)$, and a classical solution $ρ$ on $[0,1)$ whose density gradient and spatial velocity gradient diverge in $L^\infty$ as $t\uparrow 1$. Nevertheless, $ρ(t)$ converges in $C^η$ for every $0\leqη<1$.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213430106