On continuity properties of semigroups in real interpolation spaces
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AbstractStarting 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 $$(X,D(A))_{\theta ,\infty }$$ ( 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 $$\mathbb {R}^d$$ R d .
Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations
1997 ◽
Vol 7
(5)
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pp. 475-502
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1998 ◽
Vol 8
(2)
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pp. 233-233
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2002 ◽
Vol 132
(03)
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pp. 627
2020 ◽
Vol 14
(4)
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pp. 7369-7378
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2013 ◽
Vol 40
(4)
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pp. 281-311
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