From the Growth of Sobolev Norms to Analytic Radius Lower Bounds: The Benjamin–Bona–Mahony Equation

This paper is devoted to the long time behavior of analytic radius of solutions to Benjamin–Bona–Mahony (BBM) equations with analytic initial data on the real line. New analytic radius lower bounds in large time are derived for solutions to the generalized BBM equation with an analytic nonlinear term and the fractional BBM equation. The main ingredients are quantitative estimates of the growth in time of higher order Sobolev norms of solutions. The results improve the previous works of Bona and Grujić [Math. Mod. Meth. Appl. S. 13: 345–360, 2003] and Wang [J. Geom. Anal. 33: 18, 2023].