A Priori Bounds and Weak Solutions for the Nonlinear Schrödinger Equation in Sobolev Spaces of Negative Order
نویسندگان
چکیده
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces H, for s negative but close to 0. For smooth solutions there is an a priori upper bound for the H norm of the solution, in terms of the H norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrary initial data in H.
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