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Creators/Authors contains: "Jinoh Kim, Yan Guo"

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  1. (, Peking mathematical journal)
    Consider the Landau equation with Coulomb potential in a periodic box. We develop a new L2 to L∞ framework to construct global unique solutions near Maxwellian with small L∞ norm. The first step is to establish global L2 estimates with strong velocity weight and time decay, under the assumption of L∞ bound, which is further controlled by such L2 estimates via De Giorgi’s method (Golse et al. in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(1), 253–295 (2019), Imbert and Mouhot in arXiv :1505.04608 (2015)). The second step is to employ estimates in Sp spaces to control velocity derivatives to ensure uniqueness, which is based on Hölder estimates via De Giorgi’s method (Golse et al. in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(1), 253–295 (2019), Golse and Vasseur in arXiv :1506.01908 (2015), Imbert and Mouhot in arXiv :1505.04608 (2015)). 
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