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

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

2010-03-09

arxiv.org/abs/1003.1820v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we consider exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove global existence of smooth solutions. Similar to the constant coefficients case, we show that the energy cannot concentrate at any point $(t,x)\in(0,\infty)\times\Omega$. For that purpose, following Ibrahim and Majdoub \cite{Ibrahim}, we use a geometric multiplier close to the well-known Morawetz multiplier used in the constant coefficients case. Then we use comparison theorem from Riemannian Geometry to estimate the error terms. Finally, using Strichartz inequality as in Smith and Sogge \cite{Sogge}, we get the global existence.

Affiliated with

Also associated with

No associations

Rating

Global Existence of the Critical Semilinear Wave Equations with Variable Coefficients Outside Obstacles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global Existence of the Critical Semilinear Wave Equations with Variable Coefficients Outside Obstacles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global Existence of the Critical Semilinear Wave Equations with Variable Coefficients Outside Obstacles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-454736