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The existential and uniqueness of solution for Zakharov-Kuznetsov equation. (English) Zbl 0969.35115

Summary: We consider the existence and uniqueness of a solution in \(H^s\) \((s> 2)\) to the Cauchy problem of the Zakharov-Kuznetsov equation \[ u_t+ u_{xxx}+ u_{xyy}+ uu_x= 0 \] to the Cauchy problem in \(H^s\) \((s>2)\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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