scholarly journals Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations

1997 ◽  
Vol 7 (5) ◽  
pp. 475-502 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Stokes Equations ◽  
Global Attractors ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Properties ◽  
Generalized Semiflows

scholarly journals On continuity properties of semigroups in real interpolation spaces

2020 ◽  
Author(s):  
Peer Christian Kunstmann
Keyword(s):  
Banach Space ◽  
Schrodinger Equation ◽  
Continuous Semigroup ◽  
Stokes Equations ◽  
Nonlinear Schrodinger Equation ◽  
Real Interpolation ◽  
Navier Stokes ◽  
Interpolation Spaces ◽  
Navier Stokes Equations ◽  
Continuity Properties

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 .

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