Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 233-246.doi: 10.1007/s10473-022-0113-0

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THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THE 3D COMPRESSIBLE ISOTHERMAL NAVIER-STOKES EQUATIONS

Haibo YU   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China
  • Received:2020-07-23 Revised:2021-05-26 Online:2022-02-25 Published:2022-02-24
  • Supported by:
    This work was partially supported by the National Natural Science Foundation of China (11701192).

Abstract: This paper concerns the global existence of strong solutions to the 3D compressible isothermal Navier-Stokes equations with a vacuum at infinity. Based on the special structure of the Zlotnik inequality, the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.

Key words: global strong solution, compressible isothermal Navier-Stokes equations, vacuum

CLC Number: 

  • 35Q30
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