On the low regularity of the fifth order Kadomtsev-Petviashvili I equation |
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Authors: | Wengu Chen |
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Institution: | a Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China b School of Mathematical Sciences, Laboratory of Math and Complex Systems, Ministry of Education, Beijing Normal University, Beijing 100875, China |
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Abstract: | We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as , while α∈R. We introduce an interpolated energy space Es to consider the well-posedness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in Es for 0<s?1. To obtain the local well-posedness, we present a bilinear estimate in the Bourgain space in the framework of the interpolated energy space. It crucially depends on the dyadic decomposed Strichartz estimate, the fifth order dispersive smoothing effect and maximal estimate. |
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Keywords: | 35Q53 35G25 |
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