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arXiv · 2101.11668

On the Cauchy problems associated to a ZK-KP-type family equations with a transversal fractional dispersion

Jorge Morales P.·Félix H. Soriano M.
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Abstract

In this paper we examine the well-posedness and ill-posedeness of the Cauchy problems associated to a family equations of ZK-KP-type \[ \begin{cases} u_{t}=u_{xxx}-\mathscr{H}D_{x}^{\alpha}u_{yy}+uu_{x}, \cr u(0)=\psi \in Z \end{cases} \] in anisotropic Sobolev spaces, where $1\le \alpha \le 1$, $\mathscr{H}$ is the Hilbert transform and $D_{x}^{\alpha}$ is the fractional derivative, both with respect to $x$.

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Jorge Morales P., Félix H. Soriano M.. 2021-01-27. On the Cauchy problems associated to a ZK-KP-type family equations with a transversal fractional dispersion. https://arxiv.org/abs/2101.11668

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