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.
On the Cauchy problem for higher dimensional Benjamin-Ono and Zakharov-Kuznetsov equations
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abstract
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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The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces
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.