We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via ²-decoupling. When we additionally average in time, further improvements can be obtained. Next, we apply multilinear refinements to show low regularity local well-posedness for nonlinear Schr\"odinger equations. For the cubic nonlinear Schr\"odinger equation the approach yields the sharp local well-posedness result.
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Robert Schippa (2024) studied this question.
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