109 Pages

Stokes operator and stability of stationary Navier-Stokes flows in infinite cylindrical domains [Elektronische Ressource] / von Myong Hwan Ri

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Stokes Operator and Stabilityof Stationary Navier-Stokes Flowsin Infinite Cylindrical DomainsVom Fachbereich Mathematikder Technischen Universit¨at Darmstadtzur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften(Dr. rer. nat.)genehmigteDissertationvonMyong Hwan Riaus PjoenjangReferent: Prof. Dr. Reinhard FarwigKorreferent: Prof. Dr. Matthias HieberTag der Einreichung: 20. M¨arz 2006Tag der mundlic¨ hen Prufung:¨ 20. April 2006Darmstadt 2006D17AbstractNavier-Stokesequationsininfinitecylindricaldomainshavebeenattractinggreatattention due to its theoretical and practical significance. However, in most cases,stationary Navier-Stokes problems were dealt with whereas instationary Navier-qStokes problems have been less studied. The L -approach to instationary Navier-Stokes problems is very important and convenient to analyze existence, uniquenessas well as strong energy inequality and partial regularity for solutions; to this end,the study of the Stokes operator is fundamental.Theaimofthisdissertationistogetresolventestimates, maximalregularityand∞boundedness ofH -calculus of Stokes operators in infinite cylindrical domains andtoapplythemtothestabilityofstationaryNavier-Stokesflowsininfinitecylindricaldomains.We start with a Stokes resolvent system in an infinite straight cylinder.



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Published 01 January 2006
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Language English