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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 2023Submission Checks Completed
03 Aug 2023Assigned to Editor
08 Aug 2023Review(s) Completed, Editorial Evaluation Pending
10 Sep 2023Reviewer(s) Assigned
03 Mar 20241st Revision Received
04 Mar 2024Submission Checks Completed
04 Mar 2024Assigned to Editor
09 Mar 2024Review(s) Completed, Editorial Evaluation Pending
03 Apr 2024Editorial Decision: Revise Minor
18 Apr 2024Submission Checks Completed
18 Apr 2024Assigned to Editor
18 Apr 2024Review(s) Completed, Editorial Evaluation Pending
07 Jun 2024Reviewer(s) Assigned
07 Jul 2024Submission Checks Completed
07 Jul 2024Assigned to Editor
07 Jul 2024Review(s) Completed, Editorial Evaluation Pending
18 Jul 2024Reviewer(s) Assigned
18 Aug 2024Editorial Decision: Accept