Dissipative weak solutions to compressible Navier-Stokes-Fokker-Planck systems with variable viscosity coefficients

详细信息    查看全文

• 作者：Eduard Feireisl^a ; ^{feireisl@math.cas.cz" class="auth_mail" title="E-mail the corresponding author} ; Yong Lu^b ; ^{luyong@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author} ; Endre Sü ; li^c ; ^{suli@maths.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Weak solutions ; Kinetic polymer models ; FENE chain ; Compressible Navier&ndash ; Stokes&ndash ; Fokker&ndash ; Planck system ; Nonhomogeneous dilute polymer ; Variable viscosity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：443
• 期：1
• 页码：322-351
• 全文大小：594 K

文摘

Motivated by a recent paper by Barrett and Süli (2016) [6], we consider the compressible Navier–Stokes system coupled with a Fokker–Planck type equation describing the motion of polymer molecules in a viscous compressible fluid occupying a bounded spatial domain, with polymer-number-density-dependent viscosity coefficients. The model arises in the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The motion of the solvent is governed by the unsteady, compressible, barotropic Navier–Stokes system, where the viscosity coefficients in the Newtonian stress tensor depend on the polymer number density. Our goal is to show that the existence theory developed in the case of constant viscosity coefficients can be extended to the case of polymer-number-density-dependent viscosities, provided that certain technical restrictions are imposed, relating the behavior of the viscosity coefficients and the pressure for large values of the solvent density. As a first step in this direction, we prove here the weak sequential stability of the family of dissipative (finite-energy) weak solutions to the system.