Global existence of classical solutions for some Oldroyd-B model via the incompressible limit (Q867438)

This paper deals with a viscoelastic model, called the Oldroyd-B model. Fluids of this type have memory. The author proves that classical local solutions of the considered problem exist for sufficiently small disturbances from the general incompressible initial data. Then, uniform stability estimates and local existence of the solutions of the compressible system are obtained. Dispersive energy estimates allow to obtain a global solution for the incompressible Oldroyd system.