In this paper, we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations. To be more precise, under some conditions on the swirling component of vorticity, we can conclude that the weak solutions are regular.
Yu DONG
,
Yaofang HUANG
,
Li LI
,
Qing LU
. THE REGULARITY CRITERIA OF WEAK SOLUTIONS TO 3D AXISYMMETRIC INCOMPRESSIBLE BOUSSINESQ EQUATIONS*[J]. Acta mathematica scientia, Series B, 2023
, 43(6)
: 2387
-2397
.
DOI: 10.1007/s10473-023-0604-7
[1] Abidi H, Zhang P. On the global well-posedness of 3-D Boussinesq system with variable viscosity. Chinese Ann Math Ser B, 2019, 40(5): 643-688
[2] Bahouri H, Chemin J Y, Danchin R.Fourier Analysis and Nonlinear Partial Differential Equations. Berlin Heidelberg: Springer, 2011
[3] Barbagallo A, Gala S, Ragusa M A, Théra M. On the regularity of weak solutions of the Boussinesq equations in Besov spaces. Vietnam J Math, 2021, 49(3): 637-649
[4] Chae D, Lee J H.On the regularity of the axisymmetric solutions of the Navier-Stokes equations. Math Z, 2002, 239(4): 645-671
[5] Cheng F, Xu C J. Analytical smoothing effect of solution for the Boussinesq equations. Acta Math Sci, 2019, 39B(1): 165-179
[6] Guo Z G, Kučera P, Skalák Z. Regularity criterion for solutions to the Navier Stokes equations in the whole 3D space based on two vorticity components. J Math Anal Appl, 2018, 458(1): 755-766
[7] Guo Z G, Wang Y, Li Y P. Regularity criteria of axisymmetric weak solutions to the 3D MHD equations. J Math Phys, 2021, 62(12): 121502
[8] Hanachi A, Houamed H, Zerguine M. On the global well-posedness of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. Discrete Contin Dyn Syst, 2020, 40(11): 6473-6506
[9] Hmidi T, Rousset F. Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data. Ann Inst Henri Poincaré, Anal Non Linéaire, 2010, 27(5): 1227-1246
[10] Hmidi T, Rousset F. Global well-posedness for the Euler-Boussinesq system with axisymmetric data. J Funct Anal, 2011, 260(3): 745-796
[11] Jin X T, Xiao Y L, Yu H. Global well-posedness of the 2D Boussinesq equations with partial dissipation. Acta Math Sci, 2022, 42B(4): 1293-1309
[12] Mechdene M, Gala S, Guo Z G, Ragusa M A. Logarithmical regularity criterion of the three-dimensional Boussinesq equations in terms of the pressure. Z Angew Math Phys, 2016, 67(5): Art 120
[13] Miao C X, Zheng X X. On the global well-posedness for the Boussinesq system with horizontal dissipation. Commun Math Phys, 2013, 321(1): 33-67
[14] Miao C X, Zheng X X. Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity. J Math Pures Appl, 2014, 101(6): 842-872
[15] Shang Z Y, Tang F Q. Global existence and exponential decay of strong solutions for the three-dimensional Boussinesq equations. J Inequal Appl, 2020, 2020(1): Art 50
[16] Sulaiman S. On the global existence for the axisymmetric Euler-Boussinesq system in critical Besov spaces. Asymptotic Anal, 2012, 77(1/2): 89-121
[17] Wang S, Wang Y X, Liu J T. Regularity criteria to the incompressible axisymmetric Boussinesq equations. Appl Math Lett, 2021, 112: 106800
[18] Xu F Y, Zhang Q, Zheng X X. Regularity criteria of the 3D Boussinesq equations in the Morrey-Campanato space. Acta Appl Math, 2012, 121(1): 231-240
