Naslov
A generalization of the Aubin-Lions-Simon compactness Lemma for problems on moving domains

Autori
Muha, Boris

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
IFIP TC 7 Conference 2018 on System Modelling and Optimization / - , 2018, 60-60

Skup
IFIP TC 7 Conference 2018 on System Modelling and Optimization

Mjesto i datum
Essen, Njemačka, 23.07.2018. - 27.07.2018

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Aubin-Lions-Simon lemma ; generalized Bochner spaces ; moving domains ; fluid-structure interaction

Sažetak
This work addresses an extension of the Aubin- Lions-Simon compactness result to generalized Bochner spaces L^2(0, T ; H(t)), where H(t) is a family of Hilbert spaces, parameterized by t. A compactness result of this type is needed, e.g., in the study of the existence of weak solutions to a class of nonlinear evolution problems governed by partial differential equations defined on moving domains. We identify the conditions on the regularity of the domain motion in time, i.e., on the dependence of the functions spaces on time, under which our extension of the Aubin-Lions-Simon compactness result holds. Concrete examples of the application of the new compactness theorem are presented. They include a classical problem for the incompressible, Navier-Stokes equations defined on a given non-cylindrical domain, and a class of fluid-structure interaction problems for the incompressible, Navier-Stokes equations, coupled to the elastodynamics of a Koiter shell. Both the no-slip coupling condition, and the Navier slip coupling condition, are discussed. The compactness result presented in this talk is crucial in obtaining constructive existence proofs to nonlinear, moving boundary problems, using Rothe’s method.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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