Work

The Cauchy problem for the quadratic beam equation in d ≥ 2

Year: 2025

Type: article

Abstract: The purpose of this paper is to study the Cauchy problem of the beam equation with quadratic nonlinearity. We establish the global well-posedness and scattering of small solutions in 2 ≤ d ≤ 8 with the strategy of Strichartz estimates, dispersive estimates and the method of space-time resonance. The main difficulties come from the weak dispersive estimates of beam semi-group and possible resonance. We shall utilize the observation of null structure for space-time resonance, which enables us to obtain enough decay but avoiding the degeneracies.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111041

Author: Zihao Song

Institutions: Kyoto University, Research Institute for Mathematical Sciences, Kyoto University, Nanjing University of Aeronautics and Astronautics

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

OpenAlex ID: W4409921810

FWCI:

Cites: 29

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Related to: 10