Abstract
In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data ρ0 without vacuum state.
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Supported by the NNSF of China (Grant Nos. 12171438, 11801133), the Natural Science Foundation of Henan Province (Grant No. 152300410227) and the grant from the Special Project of Basic Scientific Research Business Expenses of Zhongyuan University of Technology (Grant No. K2020TD004)
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Song, C.M., Zhang, J.L. & Wang, Y.Y. Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System. Acta. Math. Sin.-English Ser. 40, 2037–2064 (2024). https://doi.org/10.1007/s10114-024-3399-0
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DOI: https://doi.org/10.1007/s10114-024-3399-0
Keywords
- Diffuse interface model
- global solutions
- Navier–Stokes equations
- Allen–Cahn equation
- spherically symmetry