Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592837 | Journal of Functional Analysis | 2008 | 28 Pages |
Abstract
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces Hs, for s negative but close to 0. For smooth solutions there is an a priori upper bound for the Hs norm of the solution, in terms of the Hs norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrary initial data in Hs.
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Mathematics
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