Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, II

2025/03/25 by He, Daoyin, Li, Qianqian, Yin, Huicheng · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.19438

Abstract

For the 2-D semilinear wave equation with scale-invariant damping ∂_t²u-Δu+\fracμt∂_tu=|u|^p, where t≥ 1 and p>1, in the paper [T. Imai, M. Kato, H. Takamura, K. Wakasa, The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions, J. Differential Equations 269 (2020), no. 10, 8387-8424], it is conjectured that the global small data weak solution u exists when p>p_s(2+μ) =(μ+3+√(μ²+14μ+17))/(2(μ+1)) for μ∈ (0, 2) and p>p_f(2)=2 for μ≥ 2. In our previous paper, the global small solution u has been obtained for p_s(2+μ)2, p>2 or μ=1, p>p_s(μ+2)=1+√ 2.

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• Global small data weak solutions of 2-D semilinear wave equations with scale-invariant damping, III
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