Decay of solutions of diffusive Oldroyd-B system in ℝ²

2018/04/21 by La, Joonhyun
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.07894

Abstract

We show that strong solutions of 2D diffusive Oldroyd-B systems in ℝ² decay at an algebraic rate, for a large class of initial data. The main ingredient for the proof is the following fact; an Oldroyd-B system is a macroscopic closure of a Fokker-Planck-Navier-Stokes system, and the free energy of this Fokker-Planck-Navier-Stokes system decays over time. In particular, \normu_{L^∞t L²x} and \norm∇_x u_{L²t L²x} are uniformly bounded for all time.

Related

• Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
• Global well-posedness and large time behavior for the Oldroyd-B model
• Strong time regularity and decay of L^∞ solutions to 2× 2 systems of conservation laws
• Global well-posedness and large time behavior of solutions to the compressible Oldroyd-B model without stress diffusion
• Optimal decay rate for the generalized Oldroyd-B model with only stress tensor diffusion in ℝ²