The authors establish global solutions to the energy-supercritical nonlinear wave equation in R^{1+3} for initial data that decomposes into a dispersed large-L2 piece and a localized short-pulse piece, yielding global existence in all homogeneous Sobolev norms.
Christodoulou , The Formation of Shocks in 3--Dimensional Fluids, European Mathematical Society, Zu\"urich, (2007)
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Global dynamics of a supercritical wave equation in a large data regime
The authors establish global solutions to the energy-supercritical nonlinear wave equation in R^{1+3} for initial data that decomposes into a dispersed large-L2 piece and a localized short-pulse piece, yielding global existence in all homogeneous Sobolev norms.