数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (2): 416-445.doi: 10.1007/s10473-025-0209-4

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LONG TIME EXISTENCE FOR THE NON-ISENTROPIC SLIGHTLY COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE

Qiangchang Ju, Jianjun Xu*   

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2023-12-14 出版日期:2025-03-25 发布日期:2025-05-08

LONG TIME EXISTENCE FOR THE NON-ISENTROPIC SLIGHTLY COMPRESSIBLE FLUID MODEL OF KORTEWEG TYPE

Qiangchang Ju, Jianjun Xu*   

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2023-12-14 Online:2025-03-25 Published:2025-05-08
  • Contact: *Jianjun Xu, E-mail: xujianjun21@gscaep.ac.cn
  • About author:Qiangchang Ju, E-mail: ju_qiangchang@iapcm.ac.cn
  • Supported by:
    JU's work was supported by the NSFC (12131007, 12071044).

摘要: We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system. Under the conditions of slight density and temperature variations, we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists, when the Mach number is sufficiently small. Furthermore, we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.

关键词: non-isentropic compressible Navier-Stokes-Korteweg equations, low Mach number limit, long time existence, strong solution

Abstract: We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system. Under the conditions of slight density and temperature variations, we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists, when the Mach number is sufficiently small. Furthermore, we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.

Key words: non-isentropic compressible Navier-Stokes-Korteweg equations, low Mach number limit, long time existence, strong solution

中图分类号: 

  • 35D35