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Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model. (English) Zbl 1390.35007

Summary: A compressible Oldroyd-B type model with stress diffusion is derived from a compressible Navier-Stokes-Fokker-Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic, compressible, isothermal, viscous Newtonian solvent, are idealized as pairs of massless beads connected with Hookean springs. We develop a priori bounds for the model, including a logarithmic bound, which guarantee the nonnegativity of the elastic extra stress tensor, and we prove the existence of large data global-in-time finite-energy weak solutions in two space dimensions.

MSC:

35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
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