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On continuity properties of semigroups in real interpolation spaces

Kunstmann, Peer Christian

Abstract:
Starting from a bi-continuous semigroup in a Banach space X (which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation spaces between X and the domain D(A) of the generator. Of particular interest is the case (X,D(A))$_{θ}$,$_{∞}$. We obtain topologies with respect to which the induced semigroup is bi-continuous, among them topologies induced by a variety of norms. We illustrate our results with applications to a nonlinear Schrödinger equation and to the Navier–Stokes equations on $\mathbb{R}$$^{d}$.

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Verlagsausgabe §
DOI: 10.5445/IR/1000129384
Veröffentlicht am 05.02.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 1424-3199, 1424-3202
KITopen-ID: 1000129384
Erschienen in Journal of evolution equations
Verlag Springer
Vorab online veröffentlicht am 22.12.2020
Schlagwörter Bi-continuous semigroups; Real interpolation; Sectorial operators; Abstract Besov spaces; Nonlinear Schrödinger equations; Navier–Stokes equations
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Web of Science
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