Sharp $L^4$ Strichartz estimate for the Zakharov--Kuznetsov equation on $\mathbb{R}\times\mathbb{T}$

Abstract

We prove the local $L^4$ Strichartz estimate without derivative loss for the Zakharov--Kuznetsov flow on $\mathbb{R}\times\mathbb{T}$. This reaches the sharp spatial regularity endpoint and implies the embedding $X^{0,b}\hookrightarrow L^4$ for every $b>1/2$. The proof reduces the estimate to a semi-algebraic mixed-measure estimate.