Global existence of null-form wave equations in exterior domains

By Jason Metcalfe, Christopher D. Sogge. 2006

80 citations recorded by the source corpus.

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 as compared to previous works concerning wave equations in exterior domains: one no longer needs to distinguish the scaling vector field from the other admissible vector fields.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0ad1150c4147280bf918d079ea876dd948038553

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Local decay of waves on asymptotically flat stationary space-times (2009, background): “sive literature devoted to this topic and its applications; without being exhaustive we mention Strauss [43], Keel-SmithSogge [22],[23], Burq-Planchon-Stalker-Tahvildar-Zadeh [6], Metcalfe-Sogge [31],[32]. The sharp form of the estimates as well as the notations above are from MetcalfeTataru [34]; t”
Price's Law on Nonstationary Space-Times (2011, unknown): “applications; without being exhaustive we mention [59], [36], [56], [34], [35], [9], [46], [47], [58], [31].”
A new physical-space approach to decay for the wave equation with applications to black hole spacetimes (2009, unknown): “…and Sideris [11] obtained decay results by commuting only with t∂ t + r∂ r and angular momentum operators, and this, used together with integrated local decay estimates in the style of Morawetz [16], has proven useful in a number of problems concerning obstacles, multiple speeds, etc. [1, 9, 14].”