Flame spread and flame length are two of the most important characteristics to determine flame growth and heat transfer to a solid fuel. Depending on the intensity of the opposed flow, and therefore the oxidizer residence time in the burning region, flame spread can be divided into three different regimes. In the thermal regime the residence time is much larger than the chemical time of the reactions, and the flame spread is independent on the opposing flow velocity. Reducing the residence time, the flame enters in the kinetic regime where the flame eventually experiences blow-off extinction. In a quiescent environment, possible only in microgravity, oxygen can reach the flame region only by diffusion, and it might not be fast enough to guarantee the reactions to occur. In this regime, called radiative regime, the flame eventually extinguishes, since the heat losses are larger than the heat released by the reactions. In this work, the role played by the boundary layer due to very low flow velocities in the radiative regime is studied, both experimentally and computationally. Experiments were carried out on the International Space Station, using thin sheets of polymethyl-methacrylate as fuel. Parameters such as flow velocity, oxygen concentration, sample width, and fuel thickness were varied in these experiments. The flame size changes significantly as the flame spread across a developing boundary layer, as predicted by the computational model. However, over the limited range of boundary layer development length, the experiments did not completely agree with the rise in spread rate in a thinning boundary layer as expected from the simulations.