An elementary proof of the modified scattering of weak null quasilinear wave equations

Communications on Pure &amp Applied Analysis 2026 Open access

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Authors: Daoyin He, Yaqing Sun
DOI: 10.3934/cpaa.2026020
Cited by: 0
References: 4

Abstract

In this paper, we consider the Cauchy problem of 3D quasilinear wave equations which satisfy the weak null condition. First, we use Fourier transform to express the solution in terms of the profile function, and then introduce a dyadic decomposition in phase space, and, hence, by applying the space-time resonance method, we give an elementary proof of the modified scattering result of Deng and Pusateri [3]. We also improve the estimate of the error term between the solution of wave equation and the solution of the related asymptotic equation.

Fields of Study & Subjects

Advanced Mathematical Physics Problems Stability and Controllability of Differential Equations Navier-Stokes equation solutions

Publication details

Journal / source
Communications on Pure &amp Applied Analysis
Volume
29
Issue
0
Pages
127–162
Publication date
1 January 2026