{"paper":{"title":"Long time well-posdness of the Prandtl equations in Sobolev space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao-Jiang Xu (LMRS), Xu Zhang","submitted_at":"2015-11-16T07:40:59Z","abstract_excerpt":"In this paper, we study the long time well-posedness for the nonlinear Prandtl boundary layer equation on the half plane. While the initial data  are small perturbations of some monotonic shear profile, we prove the existence, uniqueness and stability of solutions in weighted Sobolev space by energy methods. The key point is that the life span of  the solution could be any large $T$ as long as its initial date is a perturbation around the monotonic shear profile of small size like  $e^{-T}$.  The nonlinear cancellation properties of  Prandtl equations under the monotonic assumption are the mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04850","kind":"arxiv","version":6},"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"}