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Global existence of weak solutions for three-dimensional compressible Navier-Stokes/Allen-Cahn systems with slip boundary conditions
Journal of Beijing University of Chemical Technology (Natural Science Edition) 2026, 53(2): 126-133
Published: 20 March 2026
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We have studied the global existence of weak solutions for compressible Navier-Stokes/Allen-Cahn (NSAC) systems with slip boundary conditions, which describe the flow of immiscible two-phase flow with diffusion interfaces. Under the conditions of limited initial energy and adiabatic constant γ > 2, the global existence of weak solutions for initial boundary value problems with Navier-slip boundary conditions is proved using the Faedo-Galerkin approximation and a weak convergence limit.

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