Barrett, John W.; Lu, Yong; Süli, Endre Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model. (English) Zbl 1390.35007 Commun. Math. Sci. 15, No. 5, 1265-1323 (2017). 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. Cited in 1 ReviewCited in 29 Documents MSC: 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35Q35 PDEs in connection with fluid mechanics 76A05 Non-Newtonian fluids Keywords:weak solution; compressible Navier-Stokes equation; Oldroyd-B model PDFBibTeX XMLCite \textit{J. W. Barrett} et al., Commun. Math. Sci. 15, No. 5, 1265--1323 (2017; Zbl 1390.35007) Full Text: DOI arXiv