{"paper":{"title":"On the lifespan of and the blowup mechanism for smooth solutions to a class of 2-D nonlinear wave equations with small initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bingbing Ding (Nanjing University), Huicheng Yin (Nanjing University), Ingo Witt (University of G\\\"ottingen)","submitted_at":"2012-10-30T12:25:09Z","abstract_excerpt":"This paper is concerned with the lifespan and the blowup mechanism for smooth solutions to the 2-D nonlinear wave equation $\\p_t^2u-\\ds\\sum_{i=1}^2\\p_i(c_i^2(u)\\p_iu)$ $=0$, where $c_i(u)\\in C^{\\infty}(\\Bbb R^n)$, $c_i(0)\\neq 0$, and $(c_1'(0))^2+(c_2'(0))^2\\neq 0$. This equation has an interesting physics background as it arises from the pressure-gradient model in compressible fluid dynamics and also in nonlinear variational wave equations. Under the initial condition $(u(0,x), \\p_tu(0,x))=(\\ve u_0(x), \\ve u_1(x))$ with $u_0(x), u_1(x)\\in C_0^{\\infty}(\\Bbb R^2)$, and $\\ve>0$ is small, we will"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7980","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"}