{"paper":{"title":"Complex bifurcations in B\\'enard-Marangoni convection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.CD","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Ivan Sudakov, Sergey Vakulenko","submitted_at":"2015-11-10T22:50:41Z","abstract_excerpt":"We study the dynamics of a system defined by the Navier-Stokes equations for a non-compressible fluid with Marangoni boundary conditions in the two dimensional case. We show that more complicated bifurcations can appear in this system for a certain nonlinear temperature profile as compared to bifurcations in the classical Rayleigh-B\\'enard and B\\'enard-Marangoni systems with simple linear vertical temperature profiles. In terms of the B\\'enard-Marangoni convection, the obtained mathematical results lead to our understanding of complex spatial patterns at a free liquid surface, which can be ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03326","kind":"arxiv","version":3},"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"}