Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.
Universality of global dynamics for the cubic wave equation
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abstract
We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behavior at the threshold of blowup.
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2026 1verdicts
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Semilinear wave equations in homothetic hyperboloidal coordinates and tail decay
Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.