Bilinear Space-time Estimates for Linearised Kp-type Equations on the Three-dimensional Torus with Applications
نویسنده
چکیده
A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this equation are obtained. Applications to the local and global well-posedness of dispersion generalised KP-II equations are discussed. Especially it is proved that the periodic boundary value problem for the original KP-II equation is locally well-posed for data in the anisotropic Sobolev spaces H xH ε y(T ), if s ≥ 1 2 and ε > 0.
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