## PDE Seminar (2016/10/14): Global existence of weak solution for volume preserving mean curvature flow via phase field method, Keisuke Takasao (The University of Tokyo)

Date
2016-10-14 16:30 - 2016-10-14 18:00
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Keisuke Takasao (The University of Tokyo)

The Allen-Cahn equation with non-local term for the volume preserving mean curvature flow studied by Rubinstein and Sternberg is well known. However, whether the solution converges to the time global weak solution of the volume preserving mean curvature flow or not is an open problem, due to the difficulty of estimates of the Lagrange multipliers. In this talk, we consider the Allen-Cahn equation with non-local term studied by Golovaty. We show the $L^2$ estimates of the Lagrange multipliers and the convergence of the Allen-Cahn equation to the volume preserving mean curvature flow. We also give the monotonicity formula for the Allen-Cahn equation.