{"paper":{"title":"A DeGiorgi type conjecture for minimal solutions to a nonlinear Stokes equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Monteil, Radu Ignat","submitted_at":"2018-04-20T09:08:59Z","abstract_excerpt":"We study the one-dimensional symmetry of solutions to the nonlinear Stokes equation $$ \\begin{cases} -\\Delta u+\\nabla W(u)=\\nabla p&\\text{in }\\mathbb{R}^d,\\\\ \\nabla\\cdot u=0&\\text{in }\\mathbb{R}^d, \\end{cases} $$ which are periodic in the $d-1$ last variables (living on the torus $\\mathbb{T}^{d-1}$) and globally minimize the corresponding energy in $\\Omega=\\mathbb{R}\\times \\mathbb{T}^{d-1}$, i.e., $$ E(u)=\\int_{\\Omega} \\frac12 |\\nabla u|^2+W(u)\\, dx, \\quad \\nabla\\cdot u=0. $$ Namely, we determine a class of nonlinear potentials $W\\geq 0$ such that any global minimizer $u$ of $E$ connecting two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07502","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"}