Time decay for the bounded mean oscillation of solutions of the Schr\"odinger and wave equations
Abstract
Let u(x,t) be the solution of the Schr\"odinger or wave equation with L2 initial data. We provide counterexamples to plausible conjectures involving the decay in t of the norm of u(t,·). 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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