9 J ul 2 01 7 DECAY ESTIMATES FOR WAVE EQUATION WITH A POTENTIAL ON EXTERIOR DOMAINS
نویسنده
چکیده
The purpose of the present paper is to establish the local energy decay estimates and dispersive estimates for 3-dimensional wave equation with a potential to the initial-boundary value problem on exterior domains. The geometrical assumptions on domains are rather general, for example non-trapping condition is not imposed in the local energy decay result. As a by-product, Strichartz estimates is obtained too.
منابع مشابه
ar X iv : m at h / 06 11 48 9 v 1 [ m at h . A P ] 1 6 N ov 2 00 6 GLOBAL EXISTENCE OF NULL - FORM WAVE EQUATIONS IN EXTERIOR DOMAINS
Abstract. We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave equation. We instead rely upon a class of Keel-Smith-Sogge estimates for the perturbed wave equation. Using this, a notable simplification is made ...
متن کاملDECAY OF SOLUTIONS OF THE TWO- DIMENSIONAL WAVE EQUATION IN EXTERIOR DOMAINS by
This report concerns the behavior, at large times, of solutions of two-dimensional wave equations in exterior regions. This behavior is related to low frequency calculations for the reduced wave equation. Both Dirichlet and Neumann boundary data are considered, and it is shown that there are differences in the two cases. The results also differ greatly from the corresponding ones in three dimen...
متن کاملDecay of solutions of the two-dimensional wave equation in exterior domains
This report concerns the behavior, at large times, of solutions of two-dimensional wave equations in exterior regions. This behavior is related to low frequency calculations for the reduced wave equation. Both Dirichlet and Neumann boundary data are considered, and it is shown that there are differences in the two cases. The results also differ greatly from the corresponding ones in three dimen...
متن کاملDecay Estimates for Variable Coefficient Wave Equations in Exterior Domains
In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.
متن کاملImproved decay for solutions to the linear wave equation on a Schwarzschild black hole
We prove that sufficiently regular solutions to the wave equation gφ = 0 on the exterior of the Schwarzschild black hole obey the estimates |φ| ≤ Cδv − 3 2 +δ + and |∂tφ| ≤ Cδv −2+δ + on a compact region of r and along the event horizon. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski spacetime. This result improves the kn...
متن کامل