{"paper":{"title":"Eigenvalues of the linearized 2D Euler equations via Birman-Schwinger and Lin's operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Shibi Vasudevan, Yuri Latushkin","submitted_at":"2018-02-06T06:24:46Z","abstract_excerpt":"We study spectral instability of steady states to the linearized 2D Euler equations on the torus written in vorticity form via certain Birman-Schwinger type operators $K_{\\lambda}(\\mu)$ and their associated 2-modified perturbation determinants $\\mathcal D(\\lambda,\\mu)$. Our main result characterizes the existence of an unstable eigenvalue to the linearized vorticity operator $L_{\\rm vor}$ in terms of zeros of the 2-modified Fredholm determinant $\\mathcal D(\\lambda,0)=\\det_{2}(I-K_{\\lambda}(0))$ associated with the Hilbert Schmidt operator $K_{\\lambda}(\\mu)$ for $\\mu=0$. As a consequence, we ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01813","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"}