{"paper":{"title":"Characterization of solutions to dissipative systems with sharp algebraic decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Brandolese (ICJ)","submitted_at":"2015-09-19T19:33:22Z","abstract_excerpt":"We characterize the set of functions $u\\_0\\in L^2(R^n)$ such that the solution of the problem $u\\_t=\\mathcal{L}u$ in $R^n\\times(0,\\infty)$ starting from $u\\_0$ satisfy upper and lower bounds of the form $c(1+t)^{-\\gamma}\\le \\|u(t)\\|\\_2\\le c'(1+t)^{-\\gamma}$.Here $\\mathcal{L}$ is in a large class of linear pseudo-differential operator  with homogeneous symbol (including the Laplacian, the fractional Laplacian, etc.). Applications to nonlinear PDEs will be discussed: in particular our characterization provides necessary and sufficient conditions on $u\\_0$ for a solution of the Navier--Stokes sys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05928","kind":"arxiv","version":2},"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"}