Global well-posedness for the KP-I equation

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Local and global well-posedness for the Ostrovsky equation (2006, background): “11) for regular initial data, we can proceed as was made in [9] to justify the conservation of the energy for KP I.”
Global well-posedness of the KP-I initial-value problem in the energy space (2007, background): “On the positive side, it is known that the KP-I initial value problem is globally well-posed in the “second” energy spaces on both R(2) (see [11], and also [15] and [16]) and T(2) (see [7]), as well as locally well-posed in larger spaces.”