Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows
Year: 2026
Type: preprint
Abstract: We consider long-time behavior of the zero-homogeneous solutions with 3-fold symmetry to the two-dimensional Euler equation. This is the remaining case in the relaxation theory of Said, Elgindi, and Murray [Ann. Sci. Éc. Norm. Supér. (4) \textbf{58} (2025), no.~4, 943--970], which treats $m$-fold symmetry solutions with $m\geq4$. We prove that every nonconstant $W^{1,p}$ solution satisfies $\|g_θ(t)\|_{L^p}\to\infty$ as $t\to\pm\infty$ for $1
Source: arXiv (Cornell University)
Authors: Cao, Daomin, Fan, Junhong, Qin, Guolin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203677087