{"paper":{"title":"$L^p$-$L^q$ Maximal Regularity for some Operators Associated with Linearized Incompressible Fluid-Rigid Body Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debayan Maity, Marius Tucsnak","submitted_at":"2017-12-01T08:08:20Z","abstract_excerpt":"We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\\mathcal{R}$ sectorial in $L^q$ for every $q\\in (1,\\infty)$, thus it has the maximal $L^p$-$L^q$ regularity property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use the results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00223","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"}