{"paper":{"title":"Some Exact Blowup Solutions to the Pressureless Euler Equations in R^N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"astro-ph.SR","authors_text":"Manwai Yuen","submitted_at":"2009-10-07T14:23:09Z","abstract_excerpt":"The pressureless Euler equations can be used as simple models of cosmology or plasma physics. In this paper, we construct the exact solutions in non-radial symmetry to the pressureless Euler equations in $R^{N}:$%  [c]{c}% \\rho(t,\\vec{x})=\\frac{f(\\frac{1}{a(t)^{s}}\\underset{i=1}{\\overset {N}{\\sum}}x_{i}^{s})}{a(t)^{N}}\\text{,}\\vec{u}(t,\\vec{x}% )=\\frac{\\overset{\\cdot}{a}(t)}{a(t)}\\vec{x}, a(t)=a_{1}+a_{2}t. \\label{eq234}%  where the arbitrary function $f\\geq0$ and $f\\in C^{1};$ $s\\geq1$, $a_{1}>0$ and $a_{2}$ are constants$.$\\newline In particular, for $a_{2}<0$, the solutions blow up on the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1272","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"}