Yuan-Jia Xiong

Strichartz estimates on two-dimensional irrational tori

We prove an $L^4$ Strichartz estimate for the dispersion $n_1^2+\alpha n_2^2$ on $\mathbb T^2$, for every $\alpha>0$. The loss is controlled by the Shannon entropy of the normalized squared Fourier coefficients and the cardinality of their support $S$. In particular, we obtain a norm loss of $(\log\#S)^{1/2}$ on fixed...