Minimal regularity solutions of semilinear generalized Tricomi equations

2016/08/05 by Ruan, Zhuoping, Witt, Ingo, Yin, Huicheng
#35L65 #35L67 #35L70 (Primary) #76N15 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.01826

Abstract

We prove the local existence and uniqueness of minimal regularity solutions u of the semilinear generalized Tricomi equation ∂_t² u-t^m Δu =F(u) with initial data (u(0,⋅), ∂_t u(0,⋅)) ∈ H^γ(\mathbb Rⁿ) × H^γ-\frac2m+2(\mathbb Rⁿ) under the assumption that |F(u)|\lesssim |u|^κ and |F'(u)| \lesssim |u|^κ-1 for some κ>1. Our results improve previous results of M. Beals [2] and of ourselves [15-17]. We establish Strichartz-type estimates for the linear generalized Tricomi operator ∂_t² -t^m Δ from which the semilinear results are derived.

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