The Cauchy Problem for the Euler-poisson System and Derivation of the Zakharov-kuznetsov Equation
نویسندگان
چکیده
We consider in this paper the rigorous justification of the ZakharovKuznetsov equation from the Euler-Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave small-amplitude limit is described by the ZakharovKuznetsov equation. This is done first in the case of cold plasma; we then show how to extend this result in presence of the isothermal pressure term with uniform estimates when this latter goes to zero.
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