On Burgers fluids

We investigate several qualitative aspects concerning the solutions to the flow of a Burgers fluid, a model that has been used to describe a variety of materials: polymeric liquids, asphalt and asphalt mixtures, and the earthʹs mantle. Continuous dependence of the solutions with respect to initial data and supply terms, uniqueness of solutions and the impossibility of localization of the solutions are proved. Exponential stability and structural stability are analysed. We also consider uniaxial shear flows. We prove instability of solutions whenever the constitutive parameters do not satisfy certain relations. Also we study the spatial behaviour of the solutions.