Special Session 87: Mathematical Insights into Phase-Field Models

Uniform higher order estimates for the sharp interface limit of a Navier-Stokes/Allen-Cahn system
Helmut Abels
University of Regensburg
Germany
Co-Author(s):    Mingwen Fei, Yadong Liu, Maximilain Moser
Abstract:
We consider the linearized system for the sharp interface limit of a Navier-Stokes/Allen-Cahn system around a suitable approximate solution. With the aid of a suitable weight taking the distance to the interface and the interfacial thickness into account we obtain optimal regularity estimates, which are uniformy in the interfacial thickness. This enables to improve previous convergence results in two space dimensions significantly and extend results to three space dimensions.