On the Well-Posedness of Reduced 3D Primitive Geostrophic Adjustment Model with Weak Dissipation

In this paper we prove the local well-posedness and global well-posedness with small initial data of the strong solution to the reduced 3D primitive geostrophic adjustment model with weak dissipation. The term reduced model means that the relevant physical quantities depend only on two spatial variables. The weak dissipation helps us overcome the ill-posedness of the original model. We also prove the global well-posedness of the strong solution to the Voigt alpha-regularization of this model, and establish the convergence of the strong solution of the Voigt alpha-regularized model to the corresponding solution of the original model. Furthermore, we derive a criterion for existence of finite-time blow-up of the original model with weak dissipation based on Voigt alpha-regularization.