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On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations

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arxiv 1903.02027 v1 pith:S2FG37ZP submitted 2019-03-05 math.AP

Robert Schippa This is my paper · ORCID
classification math.AP
keywords equationszakharov-kuznetsovbenjamin-onodimensionalequationhighertimecauchy
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A family of dispersive equations is considered which links a higher dimensional Benjamin-Ono equation and the Zakharov-Kuznetsov equation. For these fractional Zakharov-Kuznetsov equations new well-posedness results are proved using transversality and localization of time to small frequency dependent time intervals.

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  1. The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces

    math.AP 2019-08 conditional novelty 6.0 of 10

    The higher-dimensional Benjamin-Ono equation is locally well-posed in weighted Sobolev spaces up to an optimal decay threshold, with sharp unique continuation properties.

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