dorsal/arxiv
View SchemaTowards a sufficient criterion for collapse in 3D Euler equations
| Authors | E. A. Kuznetsov |
|---|---|
| Categories | |
| ArXiv ID | physics/0204080 |
| URL | https://arxiv.org/abs/physics/0204080 |
| DOI | 10.1016/S0167-2789(03)00225-2 |
Abstract
A sufficient integral criterion for a blow-up solution of the Hopf equations (the Euler equations with zero pressure) is found. This criterion shows that a certain positive integral quantity blows up in a finite time under specific initial conditions. Blow-up of this quantity means that solution of the Hopf equation in 3D can not be continued in the Sobolev space $H^2({\cal R}^3)$ for infinite time.
{
"annotation_id": "00490090-d2b7-46d5-978c-fddd0a8bd3f3",
"date_created": "2026-03-02T18:00:38.770000Z",
"date_modified": "2026-03-02T18:00:38.770000Z",
"file_hash": "5374bc6d4a96830bf575a71c1f72827f86676fb6ce104baf3c64b2a8a9c3e521",
"private": false,
"record": {
"abstract": "A sufficient integral criterion for a blow-up solution of the Hopf equations\n(the Euler equations with zero pressure) is found. This criterion shows that a\ncertain positive integral quantity blows up in a finite time under specific\ninitial conditions. Blow-up of this quantity means that solution of the Hopf\nequation in 3D can not be continued in the Sobolev space $H^2({\\cal R}^3)$ for\ninfinite time.",
"arxiv_id": "physics/0204080",
"authors": [
"E. A. Kuznetsov"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1016/S0167-2789(03)00225-2",
"title": "Towards a sufficient criterion for collapse in 3D Euler equations",
"url": "https://arxiv.org/abs/physics/0204080"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7123b646-ba45-4079-bcc6-82fc88c86960",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}