# 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}$.

 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 Nachgewiesen in ScopusWeb of ScienceDimensions
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