Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system
Abstract
In this paper, we study the vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system in a bounded domain. We first show the local existence of smooth solutions of the Euler/Allen-Cahn equations by modified Galerkin method. Then using the boundary layer function to deal with the mismatch of the boundary conditions between Navier-Stokes and Euler equations, and assuming that the energy dissipation for Navier-Stokes equation in the boundary layer goes to zero as the viscosity tends to zero, we prove that the solutions of the Navier-Stokes/Allen-Cahn system converge to that of the Euler/Allen-Cahn system in a proper small time interval. In addition, for strong solutions of the Navier-Stokes/Allen-Cahn system in 2D, the convergence rate is c\nu^{1/2}.
Keywords
Cite
@article{arxiv.1012.3529,
title = {Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system},
author = {Liyun Zhao and Boling Guo and Haiyang Huang},
journal= {arXiv preprint arXiv:1012.3529},
year = {2011}
}
Comments
19 pages