Entropy dissipation estimates for the Landau equation with Coulomb potentials
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913460137230336 |
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| author | Ji, Sehyun |
| author_facet | Ji, Sehyun |
| contents | We prove a lower bound for the entropy dissipation of the Landau equation with Coulomb potentials by a weighted Lebesgue norm $L^3_{-5/3}$. In particular, we enhance the weight exponent from $-5$, which was established by Desvillettes, to $-5/3$. Moreover, we prove that the weighted Lebesgue norm $L^3_{-5/3}$ is optimal for both exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09841 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropy dissipation estimates for the Landau equation with Coulomb potentials Ji, Sehyun Analysis of PDEs 35B45 We prove a lower bound for the entropy dissipation of the Landau equation with Coulomb potentials by a weighted Lebesgue norm $L^3_{-5/3}$. In particular, we enhance the weight exponent from $-5$, which was established by Desvillettes, to $-5/3$. Moreover, we prove that the weighted Lebesgue norm $L^3_{-5/3}$ is optimal for both exponents. |
| title | Entropy dissipation estimates for the Landau equation with Coulomb potentials |
| topic | Analysis of PDEs 35B45 |
| url | https://arxiv.org/abs/2305.09841 |