2018/11/14 by Donatella Donatelli, Donatelli, Donatella, Konstantina Trivisa +1
Chemical Engineering · Mathematics · #35Q30 #46E35 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1811.05684
openalex publication_date 2018/11/14 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
We investigate the global existence of weak solutions to a free boundary\nproblem governing the evolution of finitely extensible bead-spring chains in\ndilute polymers. We construct weak solutions of the two-phase model by\nperforming the asymptotic limit as the adiabatic exponent \γ goes to\n\∞ for a macroscopic model which arises from the kinetic theory of dilute\nsolutions of nonhomogeneous polymeric liquids. In this context the polymeric\nmolecules are idealized as bead-spring chains with finitely extensible\nnonlinear elastic (FENE) type spring potentials. This class of models involves\nthe unsteady, compressible, isentropic, isothermal Navier-Stokes system in a\nbounded domain \Ω in \ℝd, d=2, 3 coupled with a\nFokker-Planck-Smoluchowski-type diffusion equation (cf. Barrett and S "uli\n[4], [5], [9]). The convergence of these solutions, up to a subsequence, to the\nfree-boundary problem is established using weak convergence methods,\ncompactness arguments which rely on the monotonicity properties of certain\nquantities in the spirit of [19].\n