279 citations · 1.4k across the 39 of their papers we have counts for
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Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
Sebastian Herr, Daniel Tataru, Nikolay Tzvetkov
We consider the energy critical nonlinear Schrödinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds f…
Convolutions of singular measures and applications to the Zakharov system
Ioan Bejenaru, Sebastian Herr
Uniform L^2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimension. The results of Bennett-Bez are used…
Global well-posedness of the energy critical Nonlinear Schrödinger equation with small initial data in H^1(T^3)
Sebastian Herr, Daniel Tataru, Nikolay Tzvetkov
A refined trilinear Strichartz estimate for solutions to the Schrödinger equation on the flat rational torus T^3 is derived. By a suitable modification of critical function space t…
Strichartz estimates for the Schrödinger equation on polygonal domains
Matthew D. Blair, G. Austin Ford, Sebastian Herr +1
We prove Strichartz estimates with a loss of derivatives for the Schrödinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a…