7 papers
Low-regularity well-posedness for dispersive equations with derivative nonlinearity and quasi-periodic initial data
Robert Schippa
We show low-regularity well-posedness of the Korteweg-de Vries equation with spatially quasi-periodic initial data. To this end, we employ frequency-dependent time localization and…
Local smoothing for rough wave equations
Jan Rozendaal, Robert Schippa
We prove local smoothing estimates for wave equations with coefficients, relying on bilinear restriction estimates associated with rough wave propagation. In two and three…
Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows
Robert Schippa, Daniel Tataru
The goal of this paper is to prove bilinear estimates for rough dispersive evolutions satisfying non-degeneracy and transversality assumptions. The estimates generalize the s…
Decoupling for complex curves and improved decoupling for the cubic moment curve
Robert Schippa
We prove sharp -decoupling inequalities for non-degenerate complex curves via the bilinear argument due to Guo--Li--Yung--Zorin-Kranich, which in turn is inspired by the ef…
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 -…
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…