Global existence and nonexistence of the initial–boundary value problem for the dissipative Boussinesq equation

A class of multidimensional dissipative Boussinesq equations is considered. Under three different cases of initial energy, we prove the existence and uniqueness of global solutions in the energy space and provide sufficient conditions of finite time blow up solutions. The sharp result is given as E(0)d)(E(0)>d) level which is novel contribution of this paper, and new methods will be introduced and some analysis techniques are needed. In addition, the asymptotic behavior of the global solutions is studied.