{"paper":{"title":"Almost critical well-posedness for nonlinear wave equation with $Q_{\\mu\\nu}$ null forms in 2D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea R. Nahmod, Viktor Grigoryan","submitted_at":"2013-07-23T19:09:27Z","abstract_excerpt":"In this paper we prove an optimal local well-posedness result for the 1+2 dimensional system of nonlinear wave equations (NLW) with quadratic null-form derivative nonlinearities $Q_{\\mu\\nu}$. The Cauchy problem for these equations is known to be ill-possed for data in the Sobolev space $H^s$ with $s<5/4$ for all the basic null-forms, except $Q_0$. However, the scaling analysis predicts local well-posedness all the way to the critical regularity of $s_c=1$. Following Gr\\\"{u}nrock's result for the quadratic derivative NLW, we consider initial data in the Fourier-Lebesgue spaces $\\^{H}_s^r$, whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6194","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"}