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math.AP2011★ 46 cited
A general regularity theory for weak mean curvature flow
Kota Kasai, Yoshihiro Tonegawa
We give a new proof of Brakke's partial regularity theorem up to C^{1,ς} for weak varifold solutions of mean curvature flow by utilizing parabolic monotonicity formula, parabolic L…
math.AP2011★ 8 cited
Two-phase flow problem coupled with mean curvature flow
Chun Liu, Norifumi Sato, Yoshihiro Tonegawa
We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension 2 and 3. The phase boundary moves along with…