In this paper, we investigate the decay properties of the thermoelastic
Bresse system in the whole space. We consider many cases depending on
the parameters of the model and we establish new decay rates. We need to
mention here that, in some cases we don't have the regularity-loss
phenomena as in the previous works in the literature. To prove our
results, we use the energy method in the Fourier space to build a very
delicate Lyapunov functionals that give the desired results.