Vol. 296, No. 1, 2018

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ISSN: 0030-8730
Minimal regularity solutions of semilinear generalized Tricomi equations

Zhuoping Ruan, Ingo Witt and Huicheng Yin

Vol. 296 (2018), No. 1, 181–226
Abstract

We prove the local existence and uniqueness of minimal regularity solutions u of the semilinear generalized Tricomi equation t2u tmΔu = F(u) with initial data (u(0,),tu(0,)) γ(n) ×γ2(m+2)(n) under the assumptions that |F(u)||u|κ and |F(u)||u|κ1 for some κ > 1. Our results improve previous results of M. Beals and ourselves. We establish Strichartz-type estimates for the linear generalized Tricomi operator t2 tmΔ from which the semilinear results are derived.

Keywords
generalized Tricomi equation, minimal regularity, Fourier integral operators, Strichartz estimates
Mathematical Subject Classification 2010
Primary: 35L70
Secondary: 35L65
Milestones
Received: 23 March 2017
Revised: 5 November 2017
Accepted: 9 January 2018
Published: 1 May 2018
Authors
Zhuoping Ruan
Department of Mathematics
Nanjing University
Nanjing
China
Ingo Witt
Mathematical Institute
University of Göttingen
Göttingen
Germany
Huicheng Yin
School of Mathematical Sciences and Mathematical Institute
Nanjing Normal University
Nanjing
China