  In this paper, we design a novel linearized and momentum-preserving Fourier
pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With
the aid of a new semi-norm equivalence between the Fourier pseudo-spectral
method and the finite difference method, a prior bound of the numerical
solution in discrete $L^{\infty}$-norm is obtained from the discrete momentum
conservation law. Subsequently, based on the energy method and the bound of the
numerical solution, we show that, without any restriction on the mesh ratio,
the scheme is convergent with order $O(N^{-s}+\tau^2)$ in discrete
$L^\infty$-norm, where $N$ is the number of collocation points used in the
spectral method and $\tau$ is the time step. Numerical results are addressed to
confirm our theoretical analysis.
