{"paper":{"title":"On the flux problem in the theory of steady Navier-Stokes equations with nonhomogeneous boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Konstantin Pileckas, Mikhail V. Korobkov, Remigio Russo","submitted_at":"2010-09-21T09:09:31Z","abstract_excerpt":"We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $\\Omega=\\Omega_1\\setminus\\bar{\\Omega}_2, \\;\\bar\\Omega_2\\subset \\Omega_1$. We prove that this problem has a solution if the flux $\\F$ of the boundary value through $\\partial\\Omega_2$ is nonnegative. The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-side maximum principle for the total head pressure corresponding to this solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4024","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"}