Global analyticity and the lower bounds of analytic radius for the Chaplygin gas equations with source terms

Abstract

This paper is devoted to studying the global existence and the analytic radius of analytic solutions to the Chaplygin gas equations with source terms. If the initial data belongs to Gevrey spaces and it is sufficiently small, we show the solution has the global persistent property in Gevrey spaces. In particular, we obtain uniform lower bounds on the spatial analytic radius which is given by $C{e}^{-Ct}$, for some constant $C>0$, this tells us that the decay rate of the analytic radius is at most a single exponential decay, which is the slowest decay rate of lower bounds on the analytic radius compared with the double and triple exponential decay of analytic radius derived by Levermore, Bardos, et al. (see Remark 1.2). Our method is based on the Fourier transformation and Gevrey-class regularity.