Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\)

Cong He; Jingchun Chen

doi:10.56754/0719-0646.2402.0211

DOI:

https://doi.org/10.56754/0719-0646.2402.0211

Abstract

In this paper, we are concerned about the well-posedness of Vlasov-Poisson equation near vaccum in weighted Sobolev space \(W^{m, p}(w)\). The most difficult part comes from estimates of the electronic term \(\nabla_{x}\phi\). To overcome this difficulty, we establish the \(L^p\)-\(L^q\) estimates of the electronic term \(\nabla_{x}\phi\); some weight is introduced as well to obtain the off-diagonal estimate. The weight is also useful when it comes to control the higher-order derivative term.

Keywords

Vlasov-Poisson , Lp-Sobolev , weighted estimates , Lp-Lq estimates

Cong He Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA.
Jingchun Chen Department of Mathematics and Statistics, The University of Toledo, Toledo, OH 43606, USA.

Pages: 211–226
Date Published: 2022-08-22
Vol. 24 No. 2 (2022)

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