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In this paper, we study the vanishing viscosity limit for a coupledNavier-Stokes/Allen-Cahn system in a bounded domain. We first show the localexistence of smooth solutions of the Euler/Allen-Cahn equations by modifiedGalerkin method. Then using the boundary layer function to deal with themismatch of the boundary conditions between Navier-Stokes and Euler equations,and assuming that the energy dissipation for Navier-Stokes equation in theboundary layer goes to zero as the viscosity tends to zero, we prove that thesolutions of the Navier-Stokes/Allen-Cahn system converge to that of theEuler/Allen-Cahn system in a proper small time interval. In addition, forstrong solutions of the Navier-Stokes/Allen-Cahn system in 2D, the convergencerate is c\nu^{1/2}.

Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system