A receding horizon framework for stabilization of a class of infinite-dimensional controlled systems is presented. No terminal costs or constraints are used to ensure asymptotic stability of the controlled system. The key assumption is a stabilizability assumption, which can be guaranteed, for example, for the Burgers equations with periodic and with homogeneous Neumann boundary conditions. Numerical experiments validate the theoretical results. Comparisons to the case with terminal penalties acting as control Lyapunov functions are included.