Deterministic local wellposedness on R x T at s>3/4 (or s>1/2 under a low-frequency condition), shown optimal for the bilinear/Picard method, plus probabilistic wellposedness for generic H^s data with s>-1/26.
Local well-posedness for the Zakharov-Kuznetsov equation in Sobolev spaces
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The initial value problem for two-dimensional Zakharov-Kuznetsov equation on periodic boundary setting is shown to be locally well-posed in the cylinder for 9/10 < s < 1. We prove this theorem by using bilinear estimates thinking separetely the first variable and the second variable of space.
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Low regularity analysis of the Zakharov--Kuznetsov equation on $\mathbb{R} \times \mathbb{T}$
Deterministic local wellposedness on R x T at s>3/4 (or s>1/2 under a low-frequency condition), shown optimal for the bilinear/Picard method, plus probabilistic wellposedness for generic H^s data with s>-1/26.