A twisted vector-field method yields energy boundedness, local energy decay, r^p-weighted estimates, and energy and pointwise decay for waves on all spatially flat decelerated FLRW backgrounds with scale factor t^q, 0<q<1.
Finite time blow-up of semi-linear Klein-Gordon equations with positive initial energy in FLRW spacetimes
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abstract
Blowing-up solutions for semi-linear Klein-Gordon equations are considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Some sufficient conditions are shown by applying the concavity method for semi-linear wave equations in the Minkowski spacetime to semi-linear Klein-Gordon equations in FLRW spacetimes.
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Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes
A twisted vector-field method yields energy boundedness, local energy decay, r^p-weighted estimates, and energy and pointwise decay for waves on all spatially flat decelerated FLRW backgrounds with scale factor t^q, 0<q<1.