Local well-posedness of the compressible FENE dumbbell model of Warner\n type

2019/11/06 by Dominic Breit, Breit, Dominic, Prince Romeo Mensah +1
Materials Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1911.02465

openalex publication_date 2019/11/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider a dilute suspension of dumbbells joined by a finitely extendible\nnonlinear elastic (FENE) connector evolving under the classical Warner\npotential U(s)=-\(b)/(2) \log(1-\(2s)/(b)), s\∈[0,\(b)/(2)). The\nsolvent under consideration is modelled by the compressible Navier--Stokes\nsystem defined on the torus mathbbT^d with d=2,3 coupled with the\nFokker--Planck equation (Kolmogorov forward equation) for the probability\ndensity function of the dumbbell configuration. We prove the existence of a\nunique local-in-time solution to the coupled system where this solution is\nsmooth in the spacetime variables and interpreted weakly in the elongation\nvariable. Our result holds true independently of whether or not the\ncentre-of-mass diffusion term is incorporated in the Fokker--Planck equation.\n

Related

• The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids
• Global strong solutions and large time behavior to the compressible co-rotation FENE dumbbell model of polymeric flows near equilibrium
• Existence of a local strong solution to the beam-polymeric fluid interaction system
• Well-posedness for the FENE dumbbell model of polymetric flows in Besov spaces
• Vanishing viscosity limit to the FENE dumbbell model of polymeric flows