Uniqueness Result for the 3-D Navier-Stokes-Boussinesq Equations with Horizontal Dissipation

摘要

In this paper, for the 3-D Navier-Stokes-Boussinesq system with horizontal dissipation, where there is no smoothing effect on the vertical derivatives, we prove a uniqueness result of solutions (u,rho)is an element of LT infinity(H0,sxH0,1-s) with (del hu,del h rho)is an element of LT2(H0,sxH0,1-s) and s is an element of12,1. As a consequence, we improve the conditions stated in the paper Miao and Zheng (Commun Math Phys 321:33-67, 2013) in order to obtain a global well-posedness result in the case of axisymmetric initial data.