Strong Solutions for 1D Compressible Navier-Stokes/Allen-Cahn System with Phase Variable Dependent Viscosity

This paper is concerned with a non-isentropic compressible Navier-Stokes/Allen-Cahn system with phase variable dependent viscosity $\eta (\chi )={\chi }^{\alpha }$ and temperature dependent heat-conductivity $\kappa (\theta )={\theta }^{\beta }$. We show the global existence of strong solutions under some assumptions on growth exponent $\alpha$ and initial data. It is worth noting that the initial data could be large if $\alpha \ge 0$ is small, and the growth exponent $\beta >0$ can be arbitrary large.