{"paper":{"title":"Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongho Chae","submitted_at":"2013-06-25T03:15:39Z","abstract_excerpt":"In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in $\\Bbb R^N$. If we assume \"single signedness condition\" on the force, then we can show that a $C^1 (\\Bbb R^N)$ solution $(v,p)$ with $|v|^2+ |p|\\in L^{\\frac{q}{2}}(\\Bbb R^N)$, $q\\in (\\frac{3N}{N-1}, \\infty)$ is trivial, $v=0$. For the solution of of the steady Navier-Stokes equations, satisfying $v(x)\\to 0$ as $|x|\\to \\infty$, the condition $\\int_{\\Bbb R^3} |\\Delta v|^{\\frac65} dx<\\infty$, which is stronger than the important D-condition, $\\int_{\\Bbb R^3} |\\nabla v|^2 d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5839","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"}