Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations

In this paper, we obtain global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations. Our works are consistent with the corresponding works by Elgindi–Widmayer (SIAM J Math Anal 47:4672–4684, 2015) in the special case ({A=kappa=1}). In addition, our result concerning the SQG equation can be regarded as the borderline case of the work by Cannone et al. (Proc Lond Math Soc 106:650–674, 2013).