Interfaces and Free Boundaries
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Two-phase flow problem coupled with mean curvature flow
Chun Liu (1), Norifumi Sato (2) and Yoshihiro Tonegawa (3)(1) Department of Mathematics, The Pennsylvania State University, 207 Church Street SE, PA 16802, UNIVERSITY PARK, UNITED STATES
(2) Furano H.S., 076-0011, FURANO (HOKKAIDO), JAPAN
(3) Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, 060-0810, SAPPORO, JAPAN
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.
Keywords: Two-phase fluid, surface energy, varifold, phase field method