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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.13871 |
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| _version_ | 1866908273104388096 |
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| author | Guanghui, Jin Zhang, Huali |
| author_facet | Guanghui, Jin Zhang, Huali |
| contents | In this paper, we study the Cauchy problem for the Chern-Simons gauged $O(3)$ sigma model under the Lorenz gauge condition. We prove the local well-posedness of solutions if the initial matter field and gauge field satisfy $(\bmϕ_0, \bA_0) \in H^s(\R^2)\times H^{s-\frac12}(\R^2)$, $s>1$, where the critical regularity for $\bmϕ_0$ is $s_c=1$. Our proof is based on identifying null forms within the system and utilizing bilinear estimates in wave-Sobolev space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local well-posedness for Chern-Simons gauged $O(3)$ sigma equations under the Lorenz gauge Guanghui, Jin Zhang, Huali Analysis of PDEs Mathematical Physics Primary 35L15, 35Q40 In this paper, we study the Cauchy problem for the Chern-Simons gauged $O(3)$ sigma model under the Lorenz gauge condition. We prove the local well-posedness of solutions if the initial matter field and gauge field satisfy $(\bmϕ_0, \bA_0) \in H^s(\R^2)\times H^{s-\frac12}(\R^2)$, $s>1$, where the critical regularity for $\bmϕ_0$ is $s_c=1$. Our proof is based on identifying null forms within the system and utilizing bilinear estimates in wave-Sobolev space. |
| title | Local well-posedness for Chern-Simons gauged $O(3)$ sigma equations under the Lorenz gauge |
| topic | Analysis of PDEs Mathematical Physics Primary 35L15, 35Q40 |
| url | https://arxiv.org/abs/2503.13871 |