Geodesic
Well-posedness and stability for the two-phase periodic quasistationary Stokes flow
Daniel Böhme1 orcid ; Bogdan-Vasile Matioc1 orcid
1Universität Regensburg, Germany
Interfaces and free boundaries, Tome 27 (2025) no. 4, pp. 659-701

Voir la notice de l'article provenant de la source EMS Press

DOI

The two-phase horizontally periodic quasistationary Stokes flow in R2, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, parameterized as the graph of a function f=f(t), is considered in the general case when both gravity and surface tension effects are included. Using potential theory, the moving boundary problem is formulated as a fully nonlinear and nonlocal parabolic problem for the function f. Based on abstract parabolic theory, it is shown that the problem is well-posed in all subcritical spaces Hr(S), with r∈(3/2,2). Moreover, the stability properties of the flat equilibria are analyzed in dependence on the physical properties of the fluids.
DOI : 10.4171/ifb/530
Classification : 76D07, 31A10, 35B35, 35B65, 35K55
Mots-clés : periodic Stokes flow, well-posedness, stability, gravity, surface tension

Daniel Böhme  1   ; Bogdan-Vasile Matioc  1

1 Universität Regensburg, Germany 
Daniel Böhme; Bogdan-Vasile Matioc. Well-posedness and stability for the two-phase periodic quasistationary Stokes flow. Interfaces and free boundaries, Tome 27 (2025) no. 4, pp. 659-701. doi: 10.4171/ifb/530
@article{10_4171_ifb_530,
     author = {Daniel B\"ohme and Bogdan-Vasile Matioc},
     title = {Well-posedness and stability for the two-phase periodic quasistationary {Stokes} flow},
     journal = {Interfaces and free boundaries},
     pages = {659--701},
     year = {2025},
     volume = {27},
     number = {4},
     doi = {10.4171/ifb/530},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/530/}
}
TY  - JOUR
AU  - Daniel Böhme
AU  - Bogdan-Vasile Matioc
TI  - Well-posedness and stability for the two-phase periodic quasistationary Stokes flow
JO  - Interfaces and free boundaries
PY  - 2025
SP  - 659
EP  - 701
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/530/
DO  - 10.4171/ifb/530
ID  - 10_4171_ifb_530
ER  - 
%0 Journal Article
%A Daniel Böhme
%A Bogdan-Vasile Matioc
%T Well-posedness and stability for the two-phase periodic quasistationary Stokes flow
%J Interfaces and free boundaries
%D 2025
%P 659-701
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/530/
%R 10.4171/ifb/530
%F 10_4171_ifb_530

Cité par Sources :