On blow up NLS with a multiplicative noise
Abstract
It is of significant interest to understand whether a noise will speed up or prevent blow up. Under certain nondegenerate conditions, dD2005Blowup proved a multiplicative noise will speed up blow up of NLS, in the sense that, blow up can happen in any short time with positive probability. We prove that such probability is indeed quite small, and provide a large deviation type upper bound.
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