Finite-time breakdown of Euler flows from smooth, compactly supported initial data

Author: Tseng
Manuscript version: 8 October 2026

This research manuscript studies finite-time breakdown of the incompressible Euler equation on $\mathbb{R}^d$ for each fixed integer $d \geq 3$, with smooth, compactly supported, divergence-free initial data. It presents a dimension-dependent extension of a localized oscillatory construction, together with transverse evolution, pressure estimates, and summability of the initial increments in every Sobolev space.

Files

• main.pdf: typeset manuscript.
• main.tex: complete, self-contained LaTeX source, including the bibliography.

Compilation

Use a current TeX distribution with latexmk, or Tectonic. No additional source files, figures, or bibliography database are required.

latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex

Alternatively:

tectonic main.tex

Reference and authorship

The principal reference is OpenAI, Finite time blowup for the Euler equation, manuscript.

Use of artificial intelligence

All mathematical derivations in this manuscript were produced using artificial intelligence.