On Glassey’s conjecture for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Abstract

Abstract Consider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey’s conjecture for the time derivative nonlinearity. We also show blow-up results for the space derivative nonlinear term.

Keywords

• Wave equation
• Blow-up
• Lifespan
• FLRW spacetime
• Glassey’s conjecture