三维可压缩Navier-Stokes/Allen-Cahn系统滑移边界问题稳态弱解的存在性

The Existence of Steady-State Weak Solutions for the Three-Dimensional Compressible Navier-Stokes/Allen-Cahn System with Slip Boundary Conditions

摘要: 本文主要考虑了在三维空间中，带有滑移边界条件的Navier-Stokes/Allen-Cahn (NSAC)系统稳态弱解的存在性问题。通过运用Helmholtz速度分解定理、弱收敛极限和有效粘性通量的方法，证明了该系统在滑移边界条件下稳态弱解的存在性。

Abstract: In this paper, the existence of a steady-state weak solution for a Navier-Stokes/Allen-Cahn (NSAC) system with slip boundary conditions in 3D space is discussed. In this paper, the methods of Helmholtz’s velocity decomposition theorem, weak convergence limit and effective viscous flux are used to prove the existence of a steady-state weak solution under slip boundary conditions.