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

Consider the energy-critical focusing wave equation in odd space dimension$N\geq 3$. The equation has a nonzero radial stationary solution $W$, which isunique up to scaling and sign change. In this paper we prove that any radial,bounded in the energy norm solution of the equation behaves asymptotically as asum of modulated $W$s, decoupled by the scaling, and a radiation term.  The proof essentially boils down to the fact that the equation does not havepurely nonradiative multisoliton solutions. The proof overcomes the fundamentalobstruction for the extension of the 3D case (treated in our previous work,Cambridge Journal of Mathematics 2013, arXiv:1204.0031) by reducing the studyof a multisoliton solution to a finite dimensional system of ordinarydifferential equations on the modulation parameters. The key ingredient of theproof is to show that this system of equations creates some radiation,contradicting the existence of pure multisolitons.

Soliton resolution for the radial critical wave equation in all odd space dimensions