Benjamin Dodson
Published 2009-09-04, updated 2009-09-06Version 2
We prove global well-posedness for the cubic, defocusing, nonlinear Schr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \in H^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by improving the almost Morawetz estimates in [9].
Almost sure local well-posedness for cubic nonlinear Schrodinger equation with higher order operators
Global well-posedness of the 3-D full water wave problem
On the instability for the cubic nonlinear Schrodinger equation
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