98 citations · 104 across the 5 of their papers we have counts for
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Global results for weakly dispersive KP-II equations on the cylinder
Sebastian Herr, Robert Schippa, Nikolay Tzvetkov
We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sha…
Global well-posedness of the cubic nonlinear Schrödinger equation on
Sebastian Herr, Beomjong Kwak
We prove global well-posedness for the cubic nonlinear Schrödinger equation for periodic initial data in the mass-critical dimension for initial data of arbitrary size in the…
The Cauchy problem for the periodic Kadomtsev--Petviashvili--II equation below
Sebastian Herr, Robert Schippa, Nikolay Tzvetkov
We extend Bourgain's -wellposedness result for the KP-II equation on to initial data with negative Sobolev regularity. The key ingredient is a new linear -…
Strichartz estimates and global well-posedness of the cubic NLS on
Sebastian Herr, Beomjong Kwak
The optimal -Strichartz estimate for the Schr{ö}dinger equation on the two-dimensional rational torus is proved, which improves an estimate of Bourgain. A new m…
On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition
S. Herr
It is shown that the Cauchy problem for the DNLS equation in the spatially periodic setting is locally well-posed in Sobolev spaces H^s(T) for s \geq 1/2. Moreover, global well-pos…