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Wave propagation for the isentropic compressible Navier–Stokes/Allen–Cahn system.

Authors :
Chen, Yazhou
Tang, Houzhi
Zhang, Yue
Source :
Mathematical Methods in the Applied Sciences. Sep2024, p1. 17p.
Publication Year :
2024

Abstract

We study the Cauchy problem for the three‐dimensional isentropic compressible Navier–Stokes/Allen–Cahn system, which models the phase transitions in two‐component patterns interacting with a compressible fluid. Under the assumption that the initial perturbation is small and decays spatially, we establish the global existence and the pointwise behavior of strong solutions to this nonconserved system. To deal with the source terms involving the phase variable, we employ the Green's function and space‐time weighted estimates. The analysis shows that the phase variable mainly contains the diffusion wave with exponential decaying amplitude over time, and consequently the density and momentum of the compressible fluid adhere to a generalized Huygens principle. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01704214
Database :
Academic Search Index
Journal :
Mathematical Methods in the Applied Sciences
Publication Type :
Academic Journal
Accession number :
179320263
Full Text :
https://doi.org/10.1002/mma.10458