Por Adán Corcho (Universidad de Córdoba).

In this work we consider the initial value problem for the cubic Schrödinger equation, posed on cylinder $\mathbb{R}\times \mathbb{T}$, with fractional derivatives in the periodic direction. The spatial operator includes elliptic and hyperbolic regimes. We prove $L^2$ global well-posedness results in the case of higher order derivatives in the periodic direction by proving a $L^4\times L^2$ Strichartz inequality.

Further, these results remain valid on the euclidean environment $\mathbb{R}^2$, so well-posedness in $L^2$ are also achieved in this case.

Our proof in the elliptic/hyperbolic case does not work for small order derivatives in the periodic direction.

Transmissão via Zoom (pw: lisbonwade).

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.