Abstract:
We present recent results for the KP-II equations with generalized
dispersion terms, in two and three spacial dimensions, periodic only
in the x variable. We will start by showing how the solutions to the
linearized equations satisfy bilinear Strichartz-type estimates, which
are independent of the dispersion. We then use these estimates to
establish local well-posedness for the Cauchy problem associated to
the equations for low regularity data, in the framework of Bourgain
spaces. For certain ranges of dispersion, these local results are
optimal. This is a joint work with Axel Grünrock and Mahendra Panthee.
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