{"paper":{"title":"Application BMO type space to parabolic equations of Navier-Stokes type with the Neumann boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Zhang, Minghua Yang","submitted_at":"2018-03-13T04:31:00Z","abstract_excerpt":"Let $L$ be a Neumann operator of the form $L=-\\Delta_{N}$ acting on $L^2(\\mathbb R^n)$. Let ${BMO}_{\\Delta_{N}}(\\mathbb R^n)$ denote the BMO space on $\\mathbb R^n$ associated to the Neumann operator $\\L$. In this article we will show that a function $f\\in { BMO}_{\\Delta_{N}}(\\mathbb R^n)$ is the trace of the solution of $${\\mathbb L}u=u_{t}+L u=0, u(x,0)= f(x),$$\n  where $u$ satisfies a Carleson-type condition \\begin{eqnarray*}\n  \\sup_{x_B, r_B} r_B^{-n}\\int_0^{r_B^2}\\int_{B(x_B, r_B)} |\\nabla u(x,t)|^2 {dx dt } \\leq C <\\infty, \\end{eqnarray*} for some constant $C>0$. Conversely, this Carleson"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04613","kind":"arxiv","version":2},"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"}