| Abstract: |
| I consider a simple two-phase fluid model where the flow field satisfies a non-Newtonian equation in the balk and the interface moves by the normal velocity given by the normal component of the flow field plus $\kappa$ times the mean curvature of the interface itself. The model can be formally obtained as the singular perturbation limit of a coupled system involving the Allen-Cahn equation and we are particularly interested in the existence and regularity issues of the weak solution in the setting of geometric measure theory. I describe what has been attempted in this direction with some recent advances, as well as the related problems. |
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