Global solutions for a coupled compressible Navier-Stokes/Allen-Cahn system in 1D. (English) Zbl 1284.35307
Summary: In this paper, we investigate a coupled compressible Navier-Stokes/Allen-Cahn system which describes the motion of a mixture of two viscous compressible fluids. We prove the existence and uniqueness of global classical solution, the existence of weak solutions and the existence of unique strong solution of the Navier-Stokes/Allen-Cahn system in 1D for initial data \(\rho _{0}\) without vacuum states.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35D30 | Weak solutions to PDEs |
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