{"paper":{"title":"Nonlinear inviscid damping for zero mean perturbation of the 2D Euler Couette flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michele Dolce","submitted_at":"2019-03-04T21:20:57Z","abstract_excerpt":"In this note we revisit the proof of Bedrossian and Masmoudi [arXiv:1306.5028] about the inviscid damping of planar shear flows in the 2D Euler equations under the assumption of zero mean perturbation. We prove that a small perturbation to the 2D Euler Couette flow in $\\mathbb{T}\\times \\mathbb{R}$ strongly converge to zero, under the additional assumption that the average in $x$ is always zero. In general the mean is not a conserved quantity for the nonlinear dynamics, for this reason this is a particular case. Nevertheless our assumption allow the presence of echoes in the problem, which we c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01543","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"}