Kinetic and Related Models (KRM)

Global regularity for a model of Navier-Stokes equations with logarithmic sub-dissipation
Pages: 179 - 190, Issue 1, February 2018

doi:10.3934/krm.2018009      Abstract        References        Full text (393.8K)           Related Articles

Shuguang Shao - College of Applied Sciences, Beijing University of Technology, Beijing 100124, China (email)
Shu Wang - College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100124, China (email)
Wen-Qing Xu - College of Applied Sciences, Beijing University of Technology, Beijing 100124, China (email)

1 H. Bahouri, J. Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren Math. Wiss. (Fundamental Principles of Mathematical Sciences), vol. 343, Springer, Heidelberg, 2011, xvi+523pp.       
2 J.-Y. Chemin and I. Gallagher, Wellposedness and stability results for the Navier-Stokes equations in $\mathbbR^3$, Ann. Inst. H. Poincaré Anal., Non Linéaire, 26 (2009), 599-624.       
3 C. R. Doering and J. D. Gibbon, Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier-Stokes equations, Phys. D, 165 (2002), 163-175.       
4 D. Fang and B. Han, Global solution for the generalized anisotropic Navier-Stokes equations with large data, Mathematical Modeling and Analysis, 20 (2015), 205-231.       
5 C. L. Fefferman, Existence and smoothness of the Navier-Stokes equation, in: J. Carlson, et al. (Eds.), The Millennium Prize Problems, Clay Math. Inst., (2006), 57-67.       
6 I. Gallagher and M. Paicu, Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations, Proc. Amer. Math. Soc., 137 (2009), 2075-2083.       
7 T. Y. Hou and Z. Lei, On the stabilizing effect of convection in three-dimensional incompressible flows, Comm. Pure Appl. Math., 62 (2009), 501-564.       
8 T. Y. Hou, Z. Lei and C. M. Li, Global regularity of the 3D axi-symmetric Navier-Stokes equations with anisotropic data, Comm. Partial Differential Equations, 33 (2008), 1622-1637.       
9 T. Y. Hou, Z. Lei, G. Luo, S. Wang and C. Zou, On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations, Arch. Ration. Mech. Anal., 212 (2014), 683-706.       
10 T. Y. Hou and R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations, J. Nonlinear Sci., 16 (2006), 639-664.       
11 N. Katz and N. Pavlovié, A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation, Geom. Funct. Anal., 12 (2002), 355-379.       
12 N. H. Katz and N. Pavlovic, Finite time blow-up for a dyadic model of the Euler equations, Trans. Amer. Math. Soc., 357 (2005), 695-708.       
13 H. Koch and D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math., 157 (2001), 22-35.       
14 Z. Lei and F. H. Lin, Global mild solutions of Navier-Stokes equations, Comm. Pure Appl. Math., 64 (2011), 1297-1304.       
15 Z. Lei, F. H. Lin and Y. Zhou, Structure of helicity and global solutions of incompressible Navier-Stokes equation, Arch. Ration. Mech. Anal., 218 (2015), 1417-1430.       
16 Z. Lei, E. A. Navas and Q. S. Zhang, A priori bound on the velocity in axially symmetric Navier-Stokes equations, Comm. Math. Phys., 341 (2016), 289-307.       
17 D. Li and Ya. Sinai, Blow ups of complex solutions of the 3d-Navier-Stokes system and renormalization group method, J. Eur. Math. Soc., (JEMS) 10 (2008), 267-313.       
18 S. Montgomery-Smith, Finite time blow up for a Navier-Stokes like equation, Proc. Amer. Math. Soc., 129 (2001), 3025-3029.       
19 P. Plechac and V. Severak, singular and regular solutions of a nonlinear parabolic system, Nonlinearity, 16 (2003), 2083-2097.       
20 P. Plechac and V. Severak, On self-similar singular solutions of the complex Ginzburg-Landau equation, Comm. Pure Appl. Math., 54 (2001), 1215-1242.       
21 T. Tao, Localisation and compactness properties of the Navier-Stokes global regularity problem, Anal. PDE, 6 (2013), 25-107.       
22 T. Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, 2008.       
23 T. Tao, Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation, Anal. PDE, 2 (2009), 361-366.       
24 T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS Regional Conference Series in Mathematics 106, Conference Board of the Mathematical Sciences, Washington, DC, 2006.       
25 T. Tao, A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation, Dyn. Partial Differ Equ., 4 (2007), 293-302.       
26 K. Y. Wang, Global regularity for a model of three-dimensional Navier-Stokes equation, J. Differential Equations, 258 (2015), 2969-2982.       
27 Y. Zhou and Z. Lei, Logarithmically improved criteria for Euler and Navier-Stokes equations, Commun. Pure Appl. Anal., 12 (2013), 2715-2719.       

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