In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability condition.Finally,we also establish the stability of 2 D magnetic Bénard problem under 3D perturbations.
In this paper, we consider the stochastic version of the 3D Bardina model arising from the turbulent flows of fluids. We obtain the existence of probabilistie weak solution for the model with the non-Lipschitz condition.
In this paper, we consider the Cauchy problem for the 3D Leray-α model, introduced by Cheskidov et al.[11]. We obtain the global solution for the 3D Leray-α model in the fractional index Sobolev space, and prove that the 3D Leray-α model reduces to the homogeneous incompressible Navier-Stokes equations as α↓0＋, and the solution of the 3D Leray-α model will converge to the weak solution of the corresponding Navier-Stokes equations.
