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

The nonlinear wave equation $u_{tt}-\Delta u +|u_t|^{p-1}u_t=0$ is shown tobe globally well-posed in the Sobolev spaces of radially symmetric functions$H^k_{\rm rad}({\bf R}^3)\times H^{k-1}_{\rm rad}({\bf R}^3)$ for all $p\geq 3$and $k\geq 3$. Moreover, global $C^\infty $ solutions are obtained when theinitial data are $C_0^\infty$ and exponent $p$ is an odd integer. The radialsymmetry allows a reduction to the one-dimensional case where an importantobservation of A. Haraux (2009) can be applied, i.e., dissipative nonlinearwave equations contract initial data in $W^{k,q}({\bf R})\times W^{k-1,q}({\bfR})$ for all $k\in[1,2]$ and $q\in [1,\infty]$.

Global Regularity for Supercritical Nonlinear Dissipative Wave Equations in 3D