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Title: Rolls and domain walls in the Rayleigh-Bénard convection

Abstract: We investigate pattern formation in the classical Rayleigh-Bénard convection problem. We focus on rolls which are regular patterns and domain walls which are line defects arising between rolls with different orientations. The mathematical problem consists in solving the Navier-Stokes equations for the fluid velocity coupled with an additional equation for the deviation of the temperature from the conduction profile in a cylindrical domain. Our analysis relies upon a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, rolls and domain walls are found as equilibria and heteroclinic orbits, respectively, of a reduced system of ODEs.