English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Using suitable modified energies we study higher order Sobolev norms' growthin time for the nonlinear Schr\"odinger equation (NLS) on a generic $2d$ or$3d$ compact manifold. In $2d$ we extend earlier results that dealt only withcubic nonlinearities, and get polynomial in time bounds for any higher ordernonlinearities. In $3d$, we prove that solutions to the cubic NLS grow at mostexponentially, while for sub-cubic NLS we get polynomial bounds on the growthof the $H^2$-norm.

On the growth of Sobolev norms for NLS on $2d$ and $3d$ manifolds