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October, 2022 Vlasov–Poisson Equation in Besov Space
Cong He, Jingchun Chen
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Taiwanese J. Math. 26(5): 1003-1028 (October, 2022). DOI: 10.11650/tjm/220304


We study the local-in-time well-posedness of Vlasov–Poisson equation in Besov space for the large initial data. To accomplish it, we establish commutator estimates in Besov space which are quite useful in dealing with the electronic term $\nabla_{x} \phi$. Also, the $L^p$-$L^q$ type estimates for the electronic term $\nabla_{x} \phi$ are established, which are not only useful in the estimate for Poisson equation, but also play a fundamentally important role in commutator estimates involving the electronic term $\nabla_{x} \phi$.


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Cong He. Jingchun Chen. "Vlasov–Poisson Equation in Besov Space." Taiwanese J. Math. 26 (5) 1003 - 1028, October, 2022.


Received: 24 June 2021; Revised: 12 January 2022; Accepted: 15 March 2022; Published: October, 2022
First available in Project Euclid: 21 March 2022

Digital Object Identifier: 10.11650/tjm/220304

Primary: 35Q83 , 42B37
Secondary: 42B35 , 47B47

Keywords: $L^p$-$L^q$ estimates , Besov space , commutator estimates , Vlasov–Poisson equation

Rights: Copyright © 2022 The Mathematical Society of the Republic of China


Vol.26 • No. 5 • October, 2022
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