We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in $H^{s,0}({\mathbb R}^2)$ for $s>3/4$ and unconditional global well-posedness in the energy space. We also prove the global existence of perturbations with finite energy of non decaying smooth global solutions.
On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type
Gain of Regularity for the KP-I Equation
Stability of Solutions to the Quasi-Geostrophic Equations in $\mathbb R^2$
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