Volume 43 Issue 2
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JOURNAL OF MECHANICAL ENGINEERING  > 2017  >  43(2): 320-326.
SHAO Shuguang, GE Yuli, WANG Shu, XU Wenqing. Global Regularity for a Model of Inhomogeneous Three-dimensional Navier-Stokes Equations[J]. JOURNAL OF MECHANICAL ENGINEERING, 2017, 43(2): 320-326. doi: 10.11936/bjutxb2016040094
Citation: SHAO Shuguang, GE Yuli, WANG Shu, XU Wenqing. Global Regularity for a Model of Inhomogeneous Three-dimensional Navier-Stokes Equations[J]. JOURNAL OF MECHANICAL ENGINEERING, 2017, 43(2): 320-326. doi: 10.11936/bjutxb2016040094
shu

Global Regularity for a Model of Inhomogeneous Three-dimensional Navier-Stokes Equations

doi: 10.11936/bjutxb2016040094
  • 1.

    College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

  • 2.

    School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, Henan, China

  • Received Date: 28 Apr 2016
    Available Online: 13 Sep 2022
  • Issue Publish Date: 01 Feb 2017
    Abstract
  • A model of inhomogeneous three-dimensional Navier-Stokes equations was studied in this paper. By using the energy method, Littlewood-Paley paraproduct decomposition techniques and Sobolev embedding theorem study of the global regularity of solutions were adopted. The dissipative term Δu in the classical inhomogeneous Navier-Stokes equations is replaced by -D2u and a new Navier-Stokes equations model was obtained, where D was a Fourier multiplier whose symbol is m(ξ)=|ξ|5/4. Blow-up criterion and global regularity of this model were proved for the initial data (ρ0,u0)∈H3/2+ε×Hδ, where ε and δ are arbitrary small positive constants.

     

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