3维不可压Boussinesq方程在BMO^(-1)空间和各向异性Lorentz空间中的正则性准则

Regularity criteria for 3D incompressible Boussinesq equations in BMO^(-1) and anisotropic Lorentz space

主要研究3维不可压Boussinesq方程解的正则性问题,运用能量估计的方法,证明了在BMO^(-1)空间意义下涡度▽×u的正则性准则.另外,用同样的方法,还证得在各向异性Lorentz空间下关于压力π的一个正则性准则.所得结果推广了已有的结论.

It was aimed to study the regularity criterion of the solution of the 3D incompressible Boussinesq equations.By applying the thought of energy estimates,a regularity criterion of solution was established for the 3D incompressible Boussinesq equations in terms of vorticity▽×u under the framework of BMO^(-1)space.In addition,a regularity criterion about pressureπin anisotropic Lorentz space was established by the same method.The existed known results were then generalized.