Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17662 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912304345382912 |
|---|---|
| author | Dai, Wei Yang, Shiwu |
| author_facet | Dai, Wei Yang, Shiwu |
| contents | In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of singular initial data in the sense that the standard energy could be infinite and the solution may blow up at the conic point. As an application, we improve our previous result on the inverse scattering problem for the Maxwell-Klein-Gordon equations with scattering data on the future null infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characteristic initial value problem for nonlinear wave equation with singular initial data Dai, Wei Yang, Shiwu Analysis of PDEs 35L05, 35A07 In this paper, we study the characteristic initial value problem for a class of nonlinear wave equations with data on a conic light cone in the Minkowski space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class of singular initial data in the sense that the standard energy could be infinite and the solution may blow up at the conic point. As an application, we improve our previous result on the inverse scattering problem for the Maxwell-Klein-Gordon equations with scattering data on the future null infinity. |
| title | Characteristic initial value problem for nonlinear wave equation with singular initial data |
| topic | Analysis of PDEs 35L05, 35A07 |
| url | https://arxiv.org/abs/2401.17662 |