Geodesic
A moving boundary problem for periodic Stokesian Hele–Shaw flows
Joachim Escher1 ; Bogdan-Vasile Matioc2 orcid
1University of Hannover, Germany
2Leibniz University Hannover, Germany
Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 119-137

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DOI

This paper is concerned with the motion of an incompressible, viscous fluid in a Hele-Shaw cell. The free surface is moving under the influence of gravity and the fluid is modelled using a modified Darcy law for Stokesian fluids. We combine results from the theory of quasilinear elliptic equations, analytic semigroups and Fourier multipliers to prove existence of a unique classical solution to the corresponding moving boundary problem.
DOI : 10.4171/ifb/205
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Quasilinear elliptic equation, nonlinear parabolic equation, non-Newtonian fluid, Hele–Shaw flow

Joachim Escher  1   ; Bogdan-Vasile Matioc  2

1 University of Hannover, Germany
2 Leibniz University Hannover, Germany 
Joachim Escher; Bogdan-Vasile Matioc. A moving boundary problem for periodic Stokesian Hele–Shaw flows. Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 119-137. doi: 10.4171/ifb/205
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     title = {A moving boundary problem for periodic {Stokesian} {Hele{\textendash}Shaw} flows},
     journal = {Interfaces and free boundaries},
     pages = {119--137},
     year = {2009},
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     number = {1},
     doi = {10.4171/ifb/205},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/205/}
}
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