An improved Strichartz estimate for systems with divergence free data

preprint2010arXivOpen access

Abstract

Using the div-curl inequalities of Bourgain-Brezis [?MR2057026] and van Schaftingen [?MR2078071], 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 Lx1L^1_x norms of the inhomogeneity in the right hand side of the estimate.

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