Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress

Abstract

We prove global regularity of solutions of Oldroyd-B equations in 2 spatial dimensions with spatial diffusion of the polymeric stresses.

References in corpus (3)

• Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers
• Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems
• Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D

Cited by in corpus (16)

• Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
• Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
• Global solutions to the $n$-dimensional incompressible Oldroyd-B model without damping mechanism
• On diffusive 2D Fokker-Planck-Navier-Stokes systems
• Global existence in critical spaces for non Newtonian compressible viscoelastic flows
• Preserving large-scale features in simulations of elastic turbulence
• Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain
• Optimal time-decay estimates for a diffusive Oldroyd-B model
• Stress-diffusive regularizations of non-dissipative rate-type materials
• On a diffuse interface model for incompressible viscoelastic two-phase flows
• Strong Ill-Posedness in $L^{\infty }$ for the Riesz Transform Problem
• Existence and Stability of Global Solutions to a regularized Oldroyd-B Model in its Vorticity Formulation
• Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis
• Global well-posedness for two-dimensional flows of viscoelastic rate-type fluids with stress diffusion
• Ill-posedness issue on the Oldroyd-B model in the critical Besov spaces
• Global existence and long time behavior of solutions to some Oldroyd type models in hybrid Besov spaces