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In this article, we prove a bilinear estimate for Schr\"odinger equations on2d waveguide, $\mathbb{R}\times \mathbb{T}$. We hope it may be of use in thefurther study of concentration compactness for cubic NLS on $\mathbb{R}\times\mathbb{T}$.

On a bilinear restriction estimate for Schr\"odinger equations on 2D waveguide