{"paper":{"title":"On Existence and Uniqueness of the Weak Solution of a Generalized Boussinesq Equation with Press and","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Academia Sinica Beijing, Bao-Zhu Guo (Academy of Mathematics, China), DPR Korea), Gol Kim (Center of Natural Sciences, Systems Science, University of Sciences","submitted_at":"2012-07-13T08:52:54Z","abstract_excerpt":"In this paper, a generalized Boussinesq equation that couples the mass and heat flows in a viscous incompressible uid is considered. The kinematic viscosity and the heat conductivity are assumed to be dependent on the temperature. The boundary condition on the velocity of fluid is non-standard where the dynamical pressure is given on some part of the boundary, and the temperature of fluid is represented in a mixed boundary condition. The existence of the weak solution is proved by the Galerkin approximation scheme, and the uniqueness is also obtained under the condition on the weak solution th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3173","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"}