Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations

Details Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations

1997-04-07

arxiv.org/abs/math/9704212v2

Duke Math J. 91 (1998), 393-408

Mathematics

Functional Analysis

Also available at http://www.math.missouri.edu/~stephen/preprints/

Scientific paper

Let $u(x,t)$ be the solution of the Schr\"odinger or wave equation with $L_2$ initial data. We provide counterexamples to plausible conjectures involving the decay in $t$ of the $\BMO$ norm of $u(t,\cdot)$. The proofs make use of random methods, in particular, Brownian motion. (Since this paper was written, the unsolved problem remaining in this paper has been solved by Keel and Tao.)

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