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

20161014 16:30 
20161014 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Keisuke Takasao (The University of Tokyo)

 The AllenCahn equation with nonlocal 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 AllenCahn equation with nonlocal term studied by Golovaty. We show the $L^2$ estimates of the Lagrange multipliers and the convergence of the AllenCahn equation to the volume preserving mean curvature flow. We also give the monotonicity formula for the AllenCahn equation.