{"paper":{"title":"Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Manwai Yuen","submitted_at":"2010-01-03T15:20:01Z","abstract_excerpt":"In this paper, we study the blowup of the $N$-dim Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. We provide a novel integration method to show that the non-trivial classical solutions $(\\rho,V)$, with compact support in $[0,R]$, where $R>0$ is a positive constant and in the sense which $\\rho(t,r)=0$ and $V(t,r)=0$ for $r\\geq R$, under the initial condition% $H_{0}=\\int_{0}^{R}rV_{0}dr>0$ blow up on or before the finite time $T=R^{3}/(2H_{0})$ for pressureless fluids or $\\gamma>1.$\n  The main contribution of this article provides the blowup results of the Euler $(\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0380","kind":"arxiv","version":3},"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"}