Some Generalizations of the Kadomtsev]Petviashvili Equations1

The question of globalization of solutions of the Cauchy problem for some generalizations of Kadomtsev]Petviashvili equations of the form utqupuxy Dxaux.xqe uyys0, where Dxs y­x2 .1r2 and e s"1 is examined. It is shown that for esy1 and a G2, a global estimate on solutions can be derived for large initial data provided that p- 4a . A consequence of this is that if a is large 4 q a enough, the local solution in Hs R2 . can be globally continued