Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail

Jie Ji; Ling-Bing He; Yue Luo

arxiv: 2412.07287 · v4 · pith:WXWSOVROnew · submitted 2024-12-10 · 🧮 math.AP

Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in H^(-f12) space with polynomial tail

Ling-Bing He , Jie Ji , Yue Luo This is my paper

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keywords spaceequationestimatesexistencehomogeneouslandau-coulombsmoothingspatially

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We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space $H^{-\frac12}_3\cap L^1_{7}\cap L\log L$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces. The new ingredients of the proof lie in the localized techniques in both phase space and frequency space.

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