Strichartz estimates for quasi-periodic functions and applications

Abstract

We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via ${\ell }^2$-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 Schrödinger equations. For the cubic nonlinear Schrödinger equation the approach yields the sharp local well-posedness result.

28 pages