Scattering for 2D quasilinear wave equations with null conditions

Abstract

Abstract We study the scattering theory of solutions to the quasilinear wave equations with null conditions and small initial data in two dimensions. Based on the scattering profile that was described precisely in He–Liu–Wang (J. Differ. Equ. 269(4):3067–3088, 2020), we establish precise estimates for the difference of the solution and the scattering profile. Therefore, collecting the results in this paper and those in He–Liu–Wang (J. Differ. Equ. 269(4):3067–3088, 2020), we have given a basically systematic study on the long-time behavior of a small data solution to the 2D wave equation with null conditions.

Keywords

• Quasilinear wave equation
• Null conditions
• Two dimensions
• Long-time behavior
• Scattering