{"paper":{"title":"Global solvability of the Navier-Stokes equations with a free surface in the maximal $L_p\\text{-}L_q$ regularity class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hirokazu Saito","submitted_at":"2017-07-11T01:34:13Z","abstract_excerpt":"We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the $N$-dimensional Euclidean space for $N\\geq 2$ when the gravity is not taken into account. The aim of this paper is to show the global solvability of the Naiver-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal $L_p\\text{-}L_q$ regularity class. Our approach is based on the maximal $L_p\\text{-}L_q$ regularity with exponential stability for the linearized equations, and solutions to the original nonlinear problem are also exponentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03096","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"}