{"paper":{"title":"On the global existence and blowup of smooth solutions of 3-D compressible Euler equations with time-depending damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Hou (Nanjing University), Huicheng Yin (Nanjing Normal University), Ingo Witt (University of G\\\"ottingen)","submitted_at":"2015-10-15T16:35:19Z","abstract_excerpt":"In this paper, we are concerned with the global existence and blowup of smooth solutions of the 3-D compressible Euler equation with time-depending damping $$\n  \\partial_t\\rho+\\operatorname{div}(\\rho u)=0, \\quad\n  \\partial_t(\\rho u)+\\operatorname{div}\\left(\\rho u\\otimes\n  u+p\\,I_{3}\\right)=-\\,\\frac{\\mu}{(1+t)^{\\lambda}}\\,\\rho u, \\quad\n  \\rho(0,x)=\\bar \\rho+\\varepsilon\\rho_0(x),\\quad u(0,x)=\\varepsilon u_0(x), $$ where $x\\in\\mathbb R^3$, $\\mu>0$, $\\lambda\\geq 0$, and $\\bar\\rho>0$ are constants, $\\rho_0,\\, u_0\\in C_0^{\\infty}(\\mathbb R^3)$, $(\\rho_0, u_0)\\not\\equiv 0$, $\\rho(0,\\cdot)>0$, and $\\v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04613","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"}