Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 2

Global wellposedness for 2D quasilinear wave without Lorentz

Pages: 123 – 140

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n2.a2

Authors

Xinyu Cheng (School of Mathematical Sciences, Fudan University, Shanghai, China)

Dong Li (SUSTech International Center for Mathematics, and Department of Mathematics, Southern University of Science and Technology, Shenzhen, China)

Jiao Xu (SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China)

Dongbing Zha (Department of Mathematics and Institute for Nonlinear Sciences, Donghua University, Shanghai, China)

Abstract

We consider the two-dimensional quasilinear wave equations with standard null-form type quadratic nonlinearities. We introduce a new streamlined framework and prove global wellposedness without using the Lorentz boost vector fields.

Keywords

quasilinear, null form, Alinhac, Lorentz

2010 Mathematics Subject Classification

35L05, 35L15, 35L72

Full Text (PDF format)

Received 2 March 2022

Published 19 May 2022