An Improved Strichartz Estimate for Systems with Divergence Free Data

Abstract

Using the div-curl inequalities of Bourgain and Brezis [1] and van Schaftingen [9], we prove an improved Strichartz estimate for systems of inhomogeneous wave and Schrodinger equations, for which the inhomogeneity is a divergence-free vector field at each given time. The novelty of the result is that one can allow norms of the inhomogeneity in the right hand side of the estimate. Show more