|
|
| |
| Revisit of the Faddeev Model in Dimension Two* |
| |
Citation： |
Shijie DONG,Zhen LEI.Revisit of the Faddeev Model in Dimension Two*[J].Chinese Annals of Mathematics B,2022,43(5):797~818 |
| Page view： 417
Net amount： 332 |
Authors： |
Shijie DONG; Zhen LEI |
Foundation： |
National Natural Science Foundation of China (No.11725102), the China Postdoctoral Science Foundation (No.2021M690702), the National Support Program for Young Top-Notch Talents and Shanghai Science and Technology Program (Nos.21JC1400600, 19JC1420101). |
|
|
| Abstract： |
The Faddeev model is a fundamental model in relativistic quantum ?eld theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undi?erentiated wave components in the non-linearities, which somehow causes extra di?culties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou (2011) with small, regular, and compactly supported initial data, using Klainerman’s vector ?eld method enhanced by a novel angular-radial anisotropic technique. In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou (2011). The proof relies on an improved L2 norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form. |
Keywords： |
Faddeev model in R<>sup1+2, Global existence, Null condition |
Classification： |
35L05 |
|
|
Download PDF Full-Text
|
|
|
|
