On singularity formation of a 3D model for incompressible Navier–Stokes equations

Article, Preprint OPEN
Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu;

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–... View more
  • References (13)
    13 references, page 1 of 2

    [1] J. T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 94 (1984), no. 1, 61-66.

    [2] L. Caffarelli, R. Kohn and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-831.

    [3] R. J. DiPerna and P. L. Lions On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. Math. 130 (1989), 321-366.

    [4] C. Fefferman, http://www.claymath.org/millennium/Navier-Stokes equations.

    [5] T. Y. Hou and R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations, J. Nonlinear Science 16 (2006), no. 6, 639-664.

    [6] T. Y. Hou and C. Li, Global well-posedness of the viscous Boussinesq equations, Discrete and Continuous Dynamical Systems, 12 (2005), no. 1, 1-12.

    [7] T. Y. Hou and C. Li, Dynamic stability of the 3D axi-symmetric Navier-Stokes equations with swirl, Comm. Pure Appl. Math. 61 (2008), no. 5, 661-697.

    [8] T. Y. Hou and Z. Lei, On the stabilizing effect of convection in 3D incompressible Flows, Comm. Pure Appl. Math. 62 (2009), no. 4, 501-564.

    [9] T. Y. Hou and Z. Lei, On partial regularity of a 3D model of Navier-Stokes equations, Commun. Math Phys., 287 (2009), 281-298.

    [10] T. Y. Hou, C. Li, Z. Shi, S. Wang, and X. Yu, On singularity formation of a nonlinear nonlocal system, arXiv:0911.3946v1 [math.AP], 2009.

  • Related Organizations (1)
  • Metrics