Abstract
<p style='text-indent:20px;'>In this paper, we present sharp decay estimates for small data solutions to the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a modification of the vector field method for transport equation as developed by Smulevici in 2016 for the Vlasov-Poisson system. Using the Green's function in particular to estimate the bilinear terms, we improve Smulevici's result by removing the requirement of some <inline-formula><tex-math id="M1">\begin{document}$ v $\end{document}</tex-math></inline-formula>-weighted <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> integrability for the initial data and extend the result to the Vlasov-Yukawa system.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Modeling and Simulation,Numerical Analysis
Reference23 articles.
1. C. Bardos, P. Degond.Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 101-118.
2. L. Bigorgne, A vector field method for massless relativistic transport equations and applications, J. Funct. Anal., 278 (2020), 108365, 44 pp.
3. L. Bigorgne, Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes, preprint, arXiv: 2006.03579.
4. L. Bigorgne, Asymptotic properties of small data solutions of the Vlasov-Maxwell system in high dimensions, preprint, arXiv: 1712.09698.
5. L. Bigorgne.Sharp asymptotic behavior of solutions of the 3d vlasov-maxwell system with small data, Comm. Math. Phys., 376 (2020), 893-992.
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