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Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle. (English) Zbl 1060.35026
The main result of the paper is that for \(n>2\) and admissible indices, a global Minkowski Strichartz estimate holds for solutions to the Cauchy problem for the wave equation in an exterior domain. The author considers a version of the local energy decay and proves weighted Minkowski Strichartz estimations for the solutions of the homogeneous wave equation with compactly supported initial conditions. The main result follows then from a weighted Strichartz estimate to the wave equation with compactly supported initial data and forcing term.

MSC:
35B45 A priori estimates in context of PDEs
35L05 Wave equation
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