A note on pointwise convergence for the Schrödinger equation

Abstract

We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain recently proved that there is initial data, in $H^s({\mathbb{R}}^n)$ with $s<\frac{n}{2(n+1)}$, for which the solution diverges on a set of nonzero Lebesgue measure. We provide a different example enabling the generalisation to fractional Hausdorff measure.

10 pages

References in corpus (2)

• Schrödinger maximal function estimates via the pseudoconformal transformation
• A sharp Schrodinger maximal estimate in ${\mathbb{R}}^2$

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• Pointwise convergence of the Klein-Gordon flow
• The Cauchy problem for the generalized KdV equation with rough data and random data