Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation at a new critical regularity, achieved with an anisotropic two-parameter Sobolev space.
Existence of wave operators for Zakharov-Kuznetsov equation in two space dimensions
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abstract
In this paper, we study long time behavior of solution to the two dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a small global solution to the Zakharov-Kuznetsov equation which scatters to a given free solution. From this result, we have the existence of wave operators for the Zakharov-Kuznetsov equation. The proof is based on the space-time resonance method developed by Gustafson-Nakanishi-Tsai and Germain-Masmoudi-Shatah etc.
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Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation at a new critical regularity, achieved with an anisotropic two-parameter Sobolev space.