Global well-posedness of the strong solution to moist atmospheric equations with only horizontal diffusivity

In this paper, we study the three-dimensional primitive equations for atmosphere dynamics with only horizontal diffusivity. This system is considered to have full viscosities in the momentum equations, and have horizontal diffusions in the temperature equation, specific humidity equation and liquid water content equation. First, for any H2 initial data, we use energy estimate method to establish the higher order estimations of state functions in local time. Then applying the contraction mapping principle and the Aubin–Lions lemma, we obtain the well-posedness of local strong solution. Furthermore, we use a logarithmic Sobolev inequality of the limiting type and a classic logarithmic type Gronwall inequality to obtain the higher order estimations of state functions in global time. Applying the continuity method, we prove the existence and uniqueness of global strong solution.