Global weak solutions in the non-corotational Oldroyd-B case

Establish the existence of global weak solutions for the incompressible Oldroyd-B system (1.1) in the non-corotational case, namely when the parameter b is nonzero.

Background

The paper reviews prior well-posedness results for the incompressible Oldroyd-B system with velocity viscosity, stress damping, and stress diffusion as specified in system (1.1). Lions and Masmoudi had established global weak-solution existence in the corotational case b=0. The corresponding global weak-solution problem for nonzero b, which introduces the additional deformation-dependent terms in Q, is explicitly identified as unresolved.

References

In the corotational case, i.e. b = 0, Lions and Masmoudi established the existence of global weak solution in . However, the case b \neq 0 is still an open problem by now.

— Global Well-Posedness for the 3-D Inviscid Oldroyd-B Model with Fractional Stress Diffusion  (2610.21473 - Lu et al., 15 Oct 2026) in Section 1, Introduction