- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
14
2012
2
Two-phase flow problem coupled with mean curvature flow
Chun
Liu
The Pennsylvania State University, UNIVERSITY PARK, UNITED STATES
Norifumi
Sato
Furano H.S., FURANO (HOKKAIDO), JAPAN
Yoshihiro
Tonegawa
Hokkaido University, SAPPORO, JAPAN
Two-phase fluid, surface energy, varifold, phase field method
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.
Partial differential equations
Fluid mechanics
General
185
203
10.4171/IFB/279
http://www.ems-ph.org/doi/10.4171/IFB/279