The Cauchy problem for the fifth order KP equations

AbstractWe study fifth order KP equations. In 2D the global well-posedness of the Cauchy problem in the energy space for the fifth order KP-I is obtained despite the “bad sign” in the algebraic relation related to the symbol. In the case of the fifth order KP-II, global solution with data in L2(R2) for the corresponding integral equation are obtained, removing the additional condition on the data imposed in (Saut and Tzvetkov, 1999). The case of periodic boundary conditions is also considered. In 2D the local existence for data in Sobolev spaces below L2(T2) is obtained and in particular the global well-posedness for data in L2(T2). In 3D the local well-posedness for data in Sobolev spaces of low order is proven