Generalized Strauss conjecture for semilinear wave equations on ℝ³

2024/05/21 by Wang, Chengbo, Zhang, Xiaoran
#35A0 #35B33 #35B44 #35L05 #35L71 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.12761

Abstract

In this manuscript, we focus on the more delicate nonlinearity of the semilinear wave equation ∂_t² u-Δ_ℝ³u=|u|^p_Sμ(|u|) ,u(0,x)=ε u₀, u_t(0,x)=ε u₁ , where p_S=1+√(2) is the Strauss critical index in n=3, and μ is a modulus of continuity. Inspired by Chen, Reissig\citeChen₂024 and Ebert, Girardi, Reissig\citeMR4163528, we investigate the sharp condition of μ as the threshold between the global existence and blow up with small data. We obtain the almost sharp results in this paper, which in particular disproves the conjecture in \citeChen₂024.

Related

• Weighted Strichartz estimates and global existence for semilinear wave equations
• Global Solutions with Small Initial Data to Semilinear Wave Equations with Energy Supercritical Powers
• Global existence for semilinear damped wave equations in relation with the Strauss conjecture
• Blow-up of solutions to critical semilinear wave equations with variable coefficients
• Global existence for a coupled wave system related to the Strauss\n conjecture