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

In this paper we establish a complete local theory for the energy-criticalnonlinear wave equation (NLW) in high dimensions ${\mathbb R} \times {\mathbbR}^d$ with $d \geq 6$. We prove the stability of solutions under the weakcondition that the perturbation of the linear flow is small in certainspace-time norms. As a by-product of our stability analysis, we also provelocal well-posedness of solutions for which we only assume the smallness of thelinear evolution. These results provide essential technical tools that can beapplied towards obtaining the extension to high dimensions of the analysis ofKenig and Merle \cite{keme06} of the dynamics of the focusing (NLW) below theenergy threshold. By employing refined paraproduct estimates we also proveunconditional uniqueness of solutions for $d\ge 5$ in the natural energy class.This extends an earlier result by Furioli, Planchon and Terraneo \cite{FPT03}in dimension $d=4$.

Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions