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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2409.19909 |
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| _version_ | 1866913522841026560 |
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| author | Geng, Zhiyuan Wang, Changyou Yu, Junao |
| author_facet | Geng, Zhiyuan Wang, Changyou Yu, Junao |
| contents | For any $k$-dimensional smooth, compact Riemannian manifold $(N, h)\subset\mathbb R^L$ without boundary, there exists an $\varepsilon_0>0$ such that for any homogeneous of degree zero map $u_0(x)=ϕ_0(\frac{x}{|x|}):\mathbb R^n\to N$ ($n\ge 2$), if $\|\nablaϕ_0\|_{L^n(\mathbb S^{n-1})}\le\varepsilon_0$ then there is a unique solution $u:\mathbb R^n\times (0,\infty)\to N$ to the heat flow of harmonic map \eqref{HF1} and \eqref{IC}, which is forward self-similar and belongs to $C^\infty(\R^n\times (0,\infty))\cap C^{\frac1{n}}(\R^n\times [0,\infty)\setminus \{(0,0)\})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On forward self-similar heat flow of harmonic maps Geng, Zhiyuan Wang, Changyou Yu, Junao Analysis of PDEs For any $k$-dimensional smooth, compact Riemannian manifold $(N, h)\subset\mathbb R^L$ without boundary, there exists an $\varepsilon_0>0$ such that for any homogeneous of degree zero map $u_0(x)=ϕ_0(\frac{x}{|x|}):\mathbb R^n\to N$ ($n\ge 2$), if $\|\nablaϕ_0\|_{L^n(\mathbb S^{n-1})}\le\varepsilon_0$ then there is a unique solution $u:\mathbb R^n\times (0,\infty)\to N$ to the heat flow of harmonic map \eqref{HF1} and \eqref{IC}, which is forward self-similar and belongs to $C^\infty(\R^n\times (0,\infty))\cap C^{\frac1{n}}(\R^n\times [0,\infty)\setminus \{(0,0)\})$. |
| title | On forward self-similar heat flow of harmonic maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.19909 |