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A compressible Oldroyd--B type model with stress diffusion is derived from acompressible Navier--Stokes--Fokker--Planck system arising in the kinetictheory of dilute polymeric fluids, where polymer chains immersed in abarotropic, compressible, isothermal, viscous Newtonian solvent, are idealizedas pairs of massless beads connected with Hookean springs. We develop a-prioribounds for the model, including a logarithmic bound, which guarantee thenonnegativity of the elastic extra stress tensor, and we prove the existence oflarge data global-in-time finite-energy weak solutions in two space dimensions.

Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model