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

This paper studies the regularity of solutions to the Zakharov andKlein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main resultis that the nonlinear part of the solution flow falls in a smoother space thanthe initial data. This relies on a new bilinear $X^{s,b}$ estimate, which isproved using delicate dyadic and angular decompositions of the frequencydomain. Such smoothing estimates have a number of implications for thelong-term dynamics of the system. In this work, we give a simplified proof ofthe existence of global attractors for the Klein-Gordon-Schr\"{o}dinger flow inthe energy space for dimensions $d = 2,3$. Secondly, we use smoothing inconjunction with a high-low decomposition to show global well-posedness of theKlein-Gordon-Schr\"{o}dinger evolution on $\mathbb{R}^4$ below the energy spacefor sufficiently small initial data.

Smoothing for the Zakharov & Klein-Gordon-Schr\"{o}dinger Systems on Euclidean Spaces