Wave equations with low regularity coefficients

In this talk we discuss dispersive estimates for wave equations with low regularity coefficients. It was shown by Smith and Tataru that wave equations with $C^{1,1}$ coefficients satisfy the same Strichartz estimates as the unperturbed wave equation on $\mathbb{R}^n$, and that for less regular coefficients a loss of derivatives in the data occurs. We improve these results for Lipschitz coefficients with additional structural assumptions. We also discuss perturbation results through paradifferential arguments, and a recently introduced class of function spaces adapted to Fourier integral operators.