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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the nonlinear Schr\"odinger equation, $$  i\partial_{t}u+\Delta u= \mu|u|^p u, \quad (t,x)\in \mathbb{R}^{d+1}, $$ with$\mu=\pm1, p>0$.  In this work, we consider the mass-subcritical cases, that is, $p\in(0,\frac4d)$. We prove that under some restrictions on $d,p$, any radialinitial data in the critical space $\dot H^{s_c}(\mathbb{R}^d)$ with compactsupport, implies global well-posedness.

Large global solutions for nonlinear Schr\"odinger equations I, mass-subcritical cases