On continuity properties of semigroups in real interpolation spaces
Peer Christian Kunstmann · Journal of Evolution Equations · 2020
Abstract Starting from a bi-continuous semigroup in a Banach spaceX(which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation spaces betweenXand the domainD(A) of the generator. Of particular interest is the case $$(X,D(A))_{\theta ,\infty }$$ (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 $$\mathbb {R}^d$$ Rd .