We investigate the phenomenon of Landau damping within the context of the Vlasov-Riesz system. Employing a nonlinear analysis technique developed by Ionescu, Pausader, Wang, and Widmayer, our primary objective is to extend the understanding of Landau damping to kinetic models beyond the traditional Vlasov-Poisson system. Our analysis is grounded in the use of the Gevrey- norm, and we demonstrate that the critical Gevrey index =-43 +53 is dependent on the parameter from the Riesz interaction, defined as U= (-) ^- (-1). This study not only broadens the applicative scope of Landau damping but also deepens the theoretical understanding of its mechanisms in more complex kinetic frameworks.
Zhiwen Zhang (Wed,) studied this question.
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