{"paper":{"title":"Two problems in Partial Differential Equations (in Portuguese)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paulo R. Zingano","submitted_at":"2018-01-13T01:43:36Z","abstract_excerpt":"In this work, we examine two important problems in the theory of nonlinear PDEs. In Part I, we propose and solve a more general and complete version of the celebrated Leray's problem for the incompressible Navier-Stokes equations in $ \\mathbb{R}^{3} \\!$, which in its simplest form was suggested by J.$\\;$Leray in 1934 (and solved only in the 1980s by T.$\\;$ Kato, K.$\\;$Masuda and other authors). A number of related new results of clear interest to the theory of Leray's solutions are also given here.\n  In Part II, which is independent of Part I and can be read separately, we introduce an importa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04361","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"}