Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail
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| Format: | Preprint |
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2024
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| _version_ | 1866916589992935424 |
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| author | He, Ling-Bing Ji, Jie Luo, Yue |
| author_facet | He, Ling-Bing Ji, Jie Luo, Yue |
| contents | We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space $H^{-\f12}_3\cap L^1_{7}\cap L\log L$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces. As a result, we confirm that the solution exhibits a \( C^\infty \) but not \( H^\infty \) smoothing effect in the velocity variable for any positive time, when the initial data possesses a polynomial tail. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_07287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail He, Ling-Bing Ji, Jie Luo, Yue Analysis of PDEs 82B40, 35B65, 35H20 We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space $H^{-\f12}_3\cap L^1_{7}\cap L\log L$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces. As a result, we confirm that the solution exhibits a \( C^\infty \) but not \( H^\infty \) smoothing effect in the velocity variable for any positive time, when the initial data possesses a polynomial tail. |
| title | Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail |
| topic | Analysis of PDEs 82B40, 35B65, 35H20 |
| url | https://arxiv.org/abs/2412.07287 |