Lifespan estimate for semilinear wave equation in Schwarzschild spacetime

Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime

“…While the situation is completely understood in the Euclidean case with flat metric on R n , in the last years several papers have been devoted to study the semilinear wave equation in the spacetime R 1+n + equipped with different Lorentzian metrics. The semilinear wave equation in Schwarzschild has been investigated in [2,25,23,22] in the 1 + 3 dimensional case. Moreover, the wave (or Klein-Gordon) equation in de Sitter and anti -de Sitter spacetimes have been investigated in the linear and semilinear case in [41,45,42,13,7,9] and [8,44,46,47], respectively.…”

Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds

“…While for more general asymptotically Euclidean manifolds g = g 1 + g 2 , Liu-Wang [15] proved the blow-up results as well as upper bound of lifespan when 1 < q ≤ q S (n). For the Schwarzschild black hole spacetime, Lin-Lai-Ming [14] obtained blow up result for 1 < q ≤ 2, while Catania-Georgiev [1] obtained a weaker blow up result for 1 < q < q S (3). See, e.g., Zha-Zhou [24] for more discussion on exterior domains.…”

Lifespan estimates for $2$-dimensional semilinear wave equations in asymptotically Euclidean exterior domains

“…U : Zhou-Han [47] L : ? U : Lai-Zhou [15], reproved by Sobajima-Wakasa [31] We also have to mention the generalization of problem (1.8) from Euclidean space to other manifold, such as asymptotically Euclidean manifolds (see [26], [32], [38] and references therein), and black hole spacetime (see [1], [19], [21], [24] and references therein). One can find a detailed description of such kind of generalization in a recent survey paper [39].…”