{"paper":{"title":"Infinite-time Exponential Growth of the Euler Equation on Two-dimensional Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jia Shi, Zhen Lei","submitted_at":"2016-08-25T03:44:46Z","abstract_excerpt":"For any $A > 2$, we construct solutions to the two-dimensional incompressible Euler equations on the torus $\\mathbb{T}^2$ whose vorticity gradient $\\nabla\\omega$ grows exponentially in time: $$\\|\\nabla\\omega(t, \\cdot)\\|_{L^\\infty} \\gtrsim e^{At},\\quad \\forall\\ t \\geq 0.$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07010","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}