Blow up of solutions to nonlinear wave equation in 2D exterior domains

Abstract

This article proves the nonexistence of global solutions to a semilinear wave equation on an exterior domain in R 2 , which is a part of Strauss' conjecture. Mathematics Subject Classification (2010). 35L05 · 35L70.

Blow-up of solutions to critical semilinear wave equations with variable coefficients

“…The critical case p = p 0 (3) in n = 3 was obtained by Lai & Zhou [19]. For two-dimensional exterior domains, blow-up results were obtained by Li & Wang [22], when 1 < p < p 0 (2), and Lai & Zhou [21] when p = p 0 (2). Lai & Zhou also proved in [20] that p = p 0 (n) belongs to the blow-up range when n ≥ 5.…”

Finite time blow up to critical semilinear wave equation outside the ball in 3-D

“…and n ≥ 3. The blow up result for 1 < p < p c (2) was obtained by Li and Wang [10](see also [5]). When p > p c (n), it is known that we have global existence from the work of Du et al [1] for n = 4, Hidano et al [6] for n = 3, 4 and Smith, Sogge and Wang [15] for n = 2.…”

Finite time blowup of solutions to semilinear wave equation in an exterior domain

“…The upper bounds for the critical cases are shown in Lai-Zhou [8] for N = 3 and Lai-Zhou [9] for N ≥ 5. We should point out that in the two dimensional case there are some blowup results for small initial data (see Li-Wang [11] and Lai-Zhou [10]), however, precise estimates for lifespan are not treated so far.…”