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

TL;DR

This paper proves the existence of large-data, finite-energy weak solutions for a compressible Oldroyd-B model with stress diffusion, derived from kinetic theory, in two-dimensional space.

Contribution

It introduces a new derivation of the compressible Oldroyd-B model from kinetic theory and establishes global weak solutions with a priori bounds ensuring stress tensor positivity.

Findings

Existence of global weak solutions in 2D for large data.

Development of a priori bounds including a logarithmic bound.

Guarantee of nonnegativity of the elastic stress tensor.

Abstract

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.