English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This work addresses an extension of the Aubin-Lions-Simon compactness resultto generalized Bochner spaces $L^2(0,T;H(t))$, where $H(t)$ is a family ofHilbert spaces, parameterized by $t$. A compactness result of this type isneeded in the study of the existence of weak solutions to nonlinear evolutionproblems governed by partial differential equations defined on moving domains.We identify the conditions on the regularity of the domain motion in time underwhich our extension of the Aubin-Lions-Simon compactness result holds. Concreteexamples of the application of the compactness theorem are presented, includinga classical problem for the incompressible, Navier-Stokes equations defined ona {\sl given} non-cylindrical domain, and a class of fluid-structureinteraction problems for the incompressible, Navier-Stokes equations, coupledto the elastodynamics of a Koiter shell. The compactness result presented inthis manuscript is crucial in obtaining constructive existence proofs tononlinear, moving boundary problems, using Rothe's method.

A Generalization of the Aubin-Lions-Simon Compactness Lemma for Problems on Moving Domains