Existence and stability results for periodic stokesian hele-shaw flows

Joachim Escher; Bogdan-Vasile Matioc

doi:10.1137/070707671

Existence and stability results for periodic stokesian hele-shaw flows

Joachim Escher^*
, Bogdan-Vasile Matioc

^*Korrespondierende*r Autor*in für diese Arbeit

Institut für Angewandte Mathematik

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Abstract

We consider here a? 2π-periodic and two-dimensional Hele-Shaw flow modelling the motion of a viscous and incompressible fluid. The free surface is moving under the influence of gravity and is modelled by a modified Darcy law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution if the initial data is near a constant, identify the equilibria of the flow, and study their stability.

Originalsprache	Englisch
Seiten (von - bis)	1992-2006
Seitenumfang	15
Fachzeitschrift	SIAM Journal on Mathematical Analysis
Jahrgang	40
Ausgabenummer	5
DOIs	https://doi.org/10.1137/070707671
Publikationsstatus	Veröffentlicht - Okt. 2009

ASJC Scopus Sachgebiete

Analysis
Computational Mathematics
Angewandte Mathematik

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10.1137/070707671

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abstract = "We consider here a? 2π-periodic and two-dimensional Hele-Shaw flow modelling the motion of a viscous and incompressible fluid. The free surface is moving under the influence of gravity and is modelled by a modified Darcy law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution if the initial data is near a constant, identify the equilibria of the flow, and study their stability.",

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KW - Non Newtonian fluid

KW - Nonlinear parabolic equation

KW - Oldroyd-B fluid

KW - Power law fluid

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