Global Strichartz estimates for wave equations with time-dependent structured Lipschitz coefficients

Abstract

We establish global-in-time Strichartz estimates without loss of derivatives for wave equations with time-dependent Lipschitz coefficients, which satisfy an additional structural assumption. Our approach is based on a parametrix construction through the Phillips functional calculus. We furthermore obtain the well-posedness of such wave equations with Lipschitz coefficients in $H^1$.

42 pages