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On the periodic Zakharov-Kuznetsov equation

  • * Corresponding author: Tristan Robert

    * Corresponding author: Tristan Robert 

FL was partially supported by FAPERJ and CNPq Brasil, MP was partially supported by FAPESP (2016/25864-6) and CNPq (305483/2014-5) Brasil

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  • We consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on $ \mathbb T^2 $. We prove the local well-posedness for given data in $ H^s( \mathbb T^2) $ whenever $ s> 5/3 $. More importantly, we prove that this equation is of quasi-linear type for initial data in any Sobolev space on the torus, in sharp contrast with its semi-linear character in the $ \mathbb R^2 $ and $ \mathbb R\times \mathbb T $ settings.

    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35B05.


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