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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider the initial value problem for a three-component system ofquadratic nonlinear Schr\"odinger equations with mass resonance in two spacedimensions. Under a suitable condition on the coefficients of the nonlinearity,we will show that the solution decays strictly faster than $O(t^{-1})$ as $t\to +\infty$ in $L^{\infty}$ by providing with an enhanced decay estimate oforder $O((t \log t)^{-1})$. Differently from the previous works, our approachdoes not rely on the explicit form of the asymptotic profile of the solution atall.

A remark on decay rates of solutions for a system of quadratic nonlinear Schr\"odinger equations in 2D