Supercritical Zakharov–Kuznetsov equation posed on bounded rectangles


An initial boundary value problem for the 2D generalized Zakharov–Kuznetsov equation posed on a bounded rectangle is considered. Supercritical (higher than two) integer powers in nonlinearity have been studied. Results on the existence, uniqueness and exponential decay of solutions are presented.

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We appreciate very much fruitful and constructive comments and suggestions of the reviewer.

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Correspondence to G. Doronin.

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M. Castelli: Partially supported by CAPES.

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Castelli, M., Doronin, G. Supercritical Zakharov–Kuznetsov equation posed on bounded rectangles. Z. Angew. Math. Phys. 72, 37 (2021).

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  • gZK equation
  • Well-posedness
  • Exponential decay

Mathematics Subject Classification

  • 35M20
  • 35Q72