{"paper":{"title":"Global smooth solutions of 3-D quasilinear wave equations with small initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ding Bingbing, Liu Yingbo, Yin Huicheng","submitted_at":"2014-07-28T15:28:24Z","abstract_excerpt":"In this paper, we are concerned with the 3-D quasilinear wave equation $ \\ds\\sum_{i,j=0}^3g^{ij}(u, \\p u)\\p_{ij}^2u$ $=0$ with $(u(0,x), \\p_tu(0,x))=(\\ve u_0(x), \\ve u_1(x))$, where $x_0=t$, $x=(x_1, x_2, x_3)$, $\\p=(\\p_0, \\p_1, ..., \\p_3)$, $u_0(x), u_1(x)\\in C_0^\\infty(\\Bbb R^3)$, $\\ve>0$ is small enough, and $g^{ij}(u, \\p u)=g^{ji}(u, \\p u)$ are smooth in their arguments. Without loss of generality, one can write $g^{ij}(u, \\p u)=c^{ij}+d^{ij}u+\\ds\\sum_{k=0}^3e^{ij}_k\\p_ku+O(|u|^2+|\\p u|^2)$, where $c^{ij}, d^{ij}$ and $e^{ij}_k$ are some constants, and $\\ds\\sum_{i,j=0}^3c^{ij}\\p_{ij}^2=-\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7445","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"}