119 citations · 187 across the 9 of their papers we have counts for
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Power series solution of a nonlinear Schroedinger equation
Michael Christ
A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces w…
Nonuniqueness of weak solutions of the nonlinear Schroedinger equation
Michael Christ
Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schrödinger equation, with certain nonlinearities, are not unique. For any there exist…
Instability of the periodic nonlinear Schrodinger equation
Michael Christ, James Colliander, Terence Tao
We study the periodic non-linear Schrodinger equations with odd integer power nonlinearities, for initial data which are assumed to be small in some negative order Sobolev space, b…
Ill-posedness for nonlinear Schrodinger and wave equations
Michael Christ, James Colliander, Terence Tao
The nonlinear wave and Schrodinger equations on Euclidean space of any dimension, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be…