Abstract We show sharp well-posedness with analytic data-to-solution mapping in the semilinear regime for dispersion-generalized KP-I equations on R² and R T. On R² we cover the full subcritical range, whereas on R T the sharp well-posedness is strictly subcritical. We rely on linear and bilinear Strichartz estimates which are proved using decoupling techniques and square function estimates. Nonlinear Loomis-Whitney inequalities are a further ingredient. These are presently proved for Borel measures with growth condition reflecting the different geometries of the plane R², the cylinder R T, and the torus T². Finally, we point out that on tori T²_, KP-I equations are never semilinear.
Kinoshita et al. (Thu,) studied this question.