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Wave propagation for the three-dimensional isentropic compressible Navier-Stokes/Allen-Cahn system
  • Yue Zhang,
  • Yazhou Chen,
  • Houzhi Tang
Yue Zhang
Capital Normal University School of Mathematical Sciences

Corresponding Author:[email protected]

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Yazhou Chen
Beijing University of Chemical Technology College of Mathematics and Physics
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Houzhi Tang
Chinese Academy of Sciences Academy of Mathematics and Systems Science
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Abstract

In this paper, we study the Cauchy problem for the three-dimensional isentropic compressible Navier-Stokes/Allen-Cahn system, which describes the phase transitions in two-component patterns interacting with a compressible fluid. We establish the existence and space-time pointwise behaviors of global solutions to this non-conserved system. In order to control the source term consisting of the phase variable, we make use of the Green’s function and space-time weighted estimates to prove that the phase variable only contains the diffusion wave whose amplitude decays exponentially in time, so as to show that the density and momentum of the fluid obey the generalized Huygens’ principle.
03 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
03 Aug 2023Assigned to Editor
03 Aug 2023Submission Checks Completed
08 Aug 2023Review(s) Completed, Editorial Evaluation Pending
10 Sep 2023Reviewer(s) Assigned