Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces

We establish the global well-posedness of the Benjamin--Ono equation for small, zero-mean periodic initial data in the analytic Sobolev spaces $H^{\rho,s}_0$ for integer $s \ge 1$. For sufficiently small initial data, we develop a spectral rigidification mechanism that globally preserves the analyticity radius, yielding global well-posedness without continuous dynamic loss of analyticity.