Two-phase flow problem coupled with mean curvature flow

  • Chun Liu

    The Pennsylvania State University, University Park, USA
  • Norifumi Sato

    Furano H.S., Furano (Hokkaido), Japan
  • Yoshihiro Tonegawa

    Hokkaido University, Sapporo, Japan


We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension and 3. Separating two shear thickening fluids with power law viscosity strictly above critical growth , 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.

Cite this article

Chun Liu, Norifumi Sato, Yoshihiro Tonegawa, Two-phase flow problem coupled with mean curvature flow. Interfaces Free Bound. 14 (2012), no. 2, pp. 185–203

DOI 10.4171/IFB/279