JournalsaihpcVol. 38, No. 4pp. 1145–1165

Gevrey regularity for the Vlasov-Poisson system

  • Renato Velozo Ruiz

    Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK
Gevrey regularity for the Vlasov-Poisson system cover
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Abstract

We prove propagation of 1s\frac{1}{s}-Gevrey regularity (s \in (0,1)\right. for the Vlasov-Poisson system on Td×Rd\mathbb{T}^{d} \times \mathbb{R}^{d} using a Fourier space method in analogy to the results proved for the 2D-Euler system in [20] and [23]. More precisely, we give quantitative estimates for the growth of the 1s\frac{1}{s}-Gevrey norm and decay of the regularity radius for the solution of the system in terms of the force field and the volume of the support in the velocity variable of the distribution of matter. As an application, we show global existence of 1s\frac{1}{s}-Gevrey solutions (s(0,1)s \in (0,1)) for the Vlasov-Poisson system in T3×R3\mathbb{T}^{3} \times \mathbb{R}^{3}. Furthermore, the propagation of Gevrey regularity can be easily modified to obtain the same result in Rd×Rd\mathbb{R}^{d} \times \mathbb{R}^{d}. In particular, this implies global existence of analytic (s=1)(s = 1) and 1s\frac{1}{s}-Gevrey solutions (s(0,1)s \in (0,1)) for the Vlasov-Poisson system in R3×R3\mathbb{R}^{3} \times \mathbb{R}^{3}.

Cite this article

Renato Velozo Ruiz, Gevrey regularity for the Vlasov-Poisson system. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1145–1165

DOI 10.1016/J.ANIHPC.2020.10.006