, Volume 349, Issue 3, pp 599-622
Date: 19 May 2010

On the dimension of divergence sets of dispersive equations

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Abstract

We refine results of Carleson, Sjögren and Sjölin regarding the pointwise convergence to the initial data of solutions to the Schrödinger equation. We bound the Hausdorff dimension of the sets on which convergence fails. For example, with initial data in \({H^1(\mathbb{R}^{3})}\) , the sets of divergence have dimension at most one.

J. A. Barceló is supported by MEC grant MTM2008-02568, and A. Carbery and K. M. Rogers by MTM2007-60952. J. Bennett is supported by EPSRC grant EP/E022340/1.