二维不可压Boussinesq方程组有限时间内的正则性
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摘要
讨论有粘性及无粘性的二维不可压Boussinesq方程组在有限时间内的正则性问题.得到其解的爆破的两个充分性条件.
In this work,we discuss the regularity problem of inviscid and viscous two dimensional incompressible Boussinesq equations in finite time. Two sufficient conditions for the blow up of the solution are obtained.
In this work,we discuss the regularity problem of inviscid and viscous two dimensional incompressible Boussinesq equations in finite time. Two sufficient conditions for the blow up of the solution are obtained.
引文
[1]Majda A,Bertozzi A.Vorticity and incompressible flow[M].Cambridge:Cambridge University Press,2002.
[2]Chae D,Nam S K.Local existence and blow-up criterion for the Boussinesq equations[J].Proc Roy Soc Edinburgh Sect,1997,A127:935-946.
[3]Chae D.Global regularity for the 2D Boussinesq equations with partial viscousity terms[J].Adv Math,2006,203:497-513.
[4]Chae D.On the finite-time singularities of the 3D incompressible Euler equations[J].Comm Pure Appl Math,2007,60,(4):597-617.
[5]李圆.三维不可压Boussinesq方程恰当弱解奇异点集的Minkowski维数[J].湖北大学学报(自然科学版),2017,(3):241-247.
[6]Hou T Y,Li C.Global well posedness of the viscous Boussinesq equations[J].Discrete Contin Dyn Syst,2005,12(1):1-12.
[7]Danchin R,Paicu M.Global existence results for the anisotropic Boussinesq system in dimension two[J].Math Models Methods Appl Sci,2011,21(3):421-457.
[8]Larious A,Lunasin E,Titi E S.Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion[J].J Differential Equations,2013,255(9):2636-2654.
[9]Cao chongsheng,Wu jiahong.Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation[J].Arch Ration Mech Anal,2013,208(3):985-1004.
[10]Adhikari D,Cao chongsheng,Shang haifeng.Global regularity results for the 2D Boussinesq equations with partial dissipation[J].J Differential Equations,2016,260(2):1893-1917.
[11]Hmidi T,Zerguine M.On the global well-posedness of the Euler-Boussinesq system with fractional dissipation[J].Phys D,2010,239(15):1387-1401.
[12]Yang wanrong,Jiu quansen,Wu jiahong.Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation[J].J Differential Equations,2014,257(11):4188-4213.
[13]Hmidi T,Keraani S,Rousset F.Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation[J].J Differential Equations,2010,249(9):2147-2174.
[14]Hmidi T,Keraani S,Rousset F.Global well-posedness for Euler-Boussinesq system with critical dissipation[J].Comm Partial Differential Equations,2011,36(3):420-445.
[15]Fang daoyuan,Qian chenyin,Zhang ting.Global well posedness for 2D Boussinesq system with general supercrital dissipation[J].Nonlinear Analysis:Real World Applications,2016,27:326-349.
[2]Chae D,Nam S K.Local existence and blow-up criterion for the Boussinesq equations[J].Proc Roy Soc Edinburgh Sect,1997,A127:935-946.
[3]Chae D.Global regularity for the 2D Boussinesq equations with partial viscousity terms[J].Adv Math,2006,203:497-513.
[4]Chae D.On the finite-time singularities of the 3D incompressible Euler equations[J].Comm Pure Appl Math,2007,60,(4):597-617.
[5]李圆.三维不可压Boussinesq方程恰当弱解奇异点集的Minkowski维数[J].湖北大学学报(自然科学版),2017,(3):241-247.
[6]Hou T Y,Li C.Global well posedness of the viscous Boussinesq equations[J].Discrete Contin Dyn Syst,2005,12(1):1-12.
[7]Danchin R,Paicu M.Global existence results for the anisotropic Boussinesq system in dimension two[J].Math Models Methods Appl Sci,2011,21(3):421-457.
[8]Larious A,Lunasin E,Titi E S.Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion[J].J Differential Equations,2013,255(9):2636-2654.
[9]Cao chongsheng,Wu jiahong.Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation[J].Arch Ration Mech Anal,2013,208(3):985-1004.
[10]Adhikari D,Cao chongsheng,Shang haifeng.Global regularity results for the 2D Boussinesq equations with partial dissipation[J].J Differential Equations,2016,260(2):1893-1917.
[11]Hmidi T,Zerguine M.On the global well-posedness of the Euler-Boussinesq system with fractional dissipation[J].Phys D,2010,239(15):1387-1401.
[12]Yang wanrong,Jiu quansen,Wu jiahong.Global well-posedness for a class of 2D Boussinesq systems with fractional dissipation[J].J Differential Equations,2014,257(11):4188-4213.
[13]Hmidi T,Keraani S,Rousset F.Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation[J].J Differential Equations,2010,249(9):2147-2174.
[14]Hmidi T,Keraani S,Rousset F.Global well-posedness for Euler-Boussinesq system with critical dissipation[J].Comm Partial Differential Equations,2011,36(3):420-445.
[15]Fang daoyuan,Qian chenyin,Zhang ting.Global well posedness for 2D Boussinesq system with general supercrital dissipation[J].Nonlinear Analysis:Real World Applications,2016,27:326-349.