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We study the hydrodynamic scaling limit for the Glauber-Kawasaki dynamics. Itis known that, if the Kawasaki part is speeded up in a diffusive space-timescaling, one can derive the Allen-Cahn equation which is a kind of thereaction-diffusion equation in the limit. This paper concerns the scaling thatthe Glauber part, which governs the creation and annihilation of particles, isalso speeded up but slower than the Kawasaki part. Under such scaling, wederive directly from the particle system the motion by mean curvature for theinterfaces separating sparse and dense regions of particles as a combination ofthe hydrodynamic and sharp interface limits.

Motion by mean curvature from Glauber-Kawasaki dynamics