{"paper":{"title":"Mathematical analysis of long-time behavior of magnetized fluid instabilities with shear flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"physics.plasm-ph","authors_text":"Gunsu S. Yun, Hyung Ju Hwang, Youngmin Oh","submitted_at":"2017-06-25T04:55:11Z","abstract_excerpt":"We study a complex Ginzburg-Landau (GL) type model related to fluid instabilities in the boundary of magnetized toroidal plasmas (called edge-localized modes) with a prescribed shear flow on the Neumann boundary condition. We obtain the following universal results for the model in a one-dimensional interval. First, if the shear is weak, there is a unique linearly stable steady-state perturbed from the nonzero constant steady-state corresponding to the zero shear case. Second, if the shear is strong, there is no plausible steady-state except the trivial zero solution in the interval. With the h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08036","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"}