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

We consider the cubic and quintic nonlinear Schr\"{o}dinger equations (NLS)under the $\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ energy-supercritical setting.Via a newly developed unified scheme, we prove the unconditional uniqueness forsolutions to NLS at critical regularity for all dimensions. Thus, together with[18,19], the unconditional uniqueness problems for $H^{1}$-critical and$H^{1}$-supercritical cubic and quintic NLS are completely and uniformlyresolved at critical regularity for these domains. One application of ourtheorem is to prove that defocusing blowup solutions of the type in [54] is theonly possible $C([0,T);\dot{H}^{s_{c}})$ solution if exist in these domains.

The unconditional uniqueness for the energy-supercritical NLS