This short note presents the derivation of a new a priori estimate for the Oldroyd-B model. Such an estimate may provide useful information when investigating the long-time behaviour of macro-macro models, and the stability of numerical schemes. We show how this estimate can be used as a guideline to derive new estimates for other macroscopic models, like the FENE-P model.
"New entropy estimates for the Oldroyd-B model and related models." Commun. Math. Sci. 5 (4) 909 - 916, December 2007.