Dissipation estimates of the Fisher information for the Landau equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916433897717760 |
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| author | Ji, Sehyun |
| author_facet | Ji, Sehyun |
| contents | We establish an a priori estimate for the dissipation of the Fisher information for the space-homogeneous Landau equation with very soft potentials. This work is motivated by the recent breakthrough by Guillen and Silvestre, which proves that the Fisher information is monotone decreasing. As a direct consequence, we show that the Fisher information becomes instantaneously bounded, even if it is not initially bounded. This leads to a proof of the global existence of smooth solutions for the space-homogeneous Landau equation with very soft potentials, given initial data $f_0 \in L^1_{2-γ} \cap L \log L$. This result includes the case of the Coulomb potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dissipation estimates of the Fisher information for the Landau equation Ji, Sehyun Analysis of PDEs 35Q70 We establish an a priori estimate for the dissipation of the Fisher information for the space-homogeneous Landau equation with very soft potentials. This work is motivated by the recent breakthrough by Guillen and Silvestre, which proves that the Fisher information is monotone decreasing. As a direct consequence, we show that the Fisher information becomes instantaneously bounded, even if it is not initially bounded. This leads to a proof of the global existence of smooth solutions for the space-homogeneous Landau equation with very soft potentials, given initial data $f_0 \in L^1_{2-γ} \cap L \log L$. This result includes the case of the Coulomb potential. |
| title | Dissipation estimates of the Fisher information for the Landau equation |
| topic | Analysis of PDEs 35Q70 |
| url | https://arxiv.org/abs/2410.09035 |