Geodesic
Two-phase flow problem coupled with mean curvature flow
Chun Liu1 ; Norifumi Sato2 ; Yoshihiro Tonegawa3 orcid
1The Pennsylvania State University, University Park, USA
2Furano H.S., Furano (Hokkaido), Japan
3Hokkaido University, Sapporo, Japan
Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 185-203

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DOI

We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension d=2 and 3. Separating two shear thickening fluids with power law viscosity strictly above critical growth p=(d+2)/2, the phase boundary moves along with the fluid flow plus its mean curvature while exerting surface tension force to the fluid. An approximation scheme combining the Galerkin method and the phase field method is adopted.
DOI : 10.4171/ifb/279
Classification : 35-XX, 76-XX, 00-XX
Mots-clés : Two-phase fluid, surface energy, varifold, phase field method

Chun Liu  1   ; Norifumi Sato  2   ; Yoshihiro Tonegawa  3

1 The Pennsylvania State University, University Park, USA
2 Furano H.S., Furano (Hokkaido), Japan
3 Hokkaido University, Sapporo, Japan 
Chun Liu; Norifumi Sato; Yoshihiro Tonegawa. Two-phase flow problem coupled with mean curvature flow. Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 185-203. doi: 10.4171/ifb/279
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     author = {Chun Liu and Norifumi Sato and Yoshihiro Tonegawa},
     title = {Two-phase flow problem coupled with mean curvature flow},
     journal = {Interfaces and free boundaries},
     pages = {185--203},
     year = {2012},
     volume = {14},
     number = {2},
     doi = {10.4171/ifb/279},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/279/}
}
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