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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    • References(16)
  • [1]
    KAZHIKOV A V.Resolution of boundary value problems for nonhomogeneous vicous fluids[J]. Dokl Akad Nauh, 1974, 216:1008-1010.
    [2]
    SIMON J.Sur les fluides visqueux incompressibles et non homogènes[J]. C R Acad Sci Paris, 1989, 309: 447-452.
    [3]
    SIMON J.Nonhomogeneous vicous incompressible fluids: existence of velocity, density, and pressure[J]. SIAM J Math Anal, 1990, 21: 1093-1117.
    [4]
    LIONS P L.Mathematical topics in fluid mechanics: vol 1 incompressible models, oxford lecture series in mathematics and its applications[M]. New York: The Clarendon Press, Oxford University Press, 1996: 237.
    [5]
    LADYZHENSKAYA O, SOLONNIKOV V A.Unique solvability of an initial and boundary value problem for vicous incompressible nonhomogeneous fluids[J].J Soviet Math, 1978(9): 697-749.
    [6]
    PADULA M.An existence theorem for non-homogeneous incompressible fluids[J]. Rend Circ Mat Palermo, 1982, 31: 119-124.
    [7]
    SALVI R.The equations of vicous incompressible nonhomogeneous fluids: on the existence and regularity[J]. J Austral Math Soc: Ser B, 1991, 33: 94-110.
    [8]
    CHOE H J, KIM H.Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids[J]. Partial Differential Equations, 2003, 28: 1183-1201.
    [9]
    TONG L N, YUAN H J.Classical solutions to Navier-Stokes equations for nonhomogeneous incompressible fluids with non-negetive densities[J]. J Math Anal Appl, 2010, 362: 476-504.
    [10]
    FUJITA H, KATO T.On the Navier-Stokes initial value problems I[J]. Arch Rational Mech Anal, 1964, 16: 269-315.
    [11]
    DANCHIN R.Density-dependent incompressible viscous fluids in critical spaces[J]. Proc Roy Soc Edinburgh Sect A, 2003, 133: 1311-1334.
    [12]
    DANCHIN R.Local and global well-posedness results for flows of inhomogeneous viscous fluids[J].Adv Differential Equations, 2004(9): 353-386.
    [13]
    TAO T.Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation[J].Anal PDE, 2009(2): 361-366.
    [14]
    苗长兴, 吴家宏, 章志飞. Little-Paley理论及其在流体动力学方程中的应用[M]. 北京: 科学出版社, 2015: 54-56.
    [15]
    DANCHIN R.The inviscid limit for density-dependent incompressible fluids[J].Ann Fac Sci Toulouse Math, 2006(15): 637-688.
    [16]
    BAHOURI H, CHEMIN J Y, DANCHIN R.Fourier analysis and nonlinear partial differential equations[M]. Heidelberg: Springer, 2011: 343.
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