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

  • 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.
Keywords: Vlasov-Poisson, Lp-Sobolev, weighted estimates, Lp-Lq estimates

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.

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Published
2022-08-22
How to Cite
[1]
C. He and J. Chen, “Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\)”, CUBO, vol. 24, no. 2, pp. 211–226, Aug. 2022.
Section
Articles