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

In this paper, we consider exterior problem of the critical semilinear waveequation in three space dimensions with variable coefficients and prove globalexistence of smooth solutions.  Similar to the constant coefficients case, we show that the energy cannotconcentrate at any point $(t,x)\in(0,\infty)\times\Omega$. For that purpose,following Ibrahim and Majdoub \cite{Ibrahim}, we use a geometric multiplierclose to the well-known Morawetz multiplier used in the constant coefficientscase. Then we use comparison theorem from Riemannian Geometry to estimate theerror terms. Finally, using Strichartz inequality as in Smith and Sogge\cite{Sogge}, we get the global existence.

Global Existence of the Critical Semilinear Wave Equations with Variable Coefficients Outside Obstacles