Uniform vanishing damping limit for the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion

2025/12/18 by Liang, Chen, Luo, Zhaonan, Yin, Zhaoyang
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.16436

openalex publication_date 2025/12/18 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the uniform vanishing damping limit of the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion. Firstly, we find that fractional stress tensor diffusion helps to reduce the global regularity of the 2D Oldroyd-B model with damping coefficient a∈[0,1]. By virtue of improved Fourier splitting method, we then prove the optimal time decay rates under the critical regularity for a=0. When a∈ (0,1], we establish time decay rates that are uniform with respect to a. Combining the time decay rate for a∈ [0,1] and the time integrability, we obtain the uniform damping vanishing rates for the 2D Oldroyd-B model. Using spectral analysis methods, we finally improve the time decay rates for trτ with a∈ (0,1], which ensure the sharp uniform damping vanishing rates of trτ.

Citations

• Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model
• Optimal decay rate for the generalized Oldroyd-B model with only stress tensor diffusion in ℝ²
• Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
• Optimal decay rate for the 2-D compressible Oldroyd-B and Hall-MHD model
• High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation
• Global small solutions of 3D incompressible Oldroyd-B model without damping mechanism
• Global solutions to the Oldroyd-B model with a class of large initial data
• Global Regularity for some Oldroyd-B type Models
• Remarks on the Blowup Criteria for Oldroyd Models
• On the formulation of rheological equations of state
• Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type

Related

• Optimal decay rate for the generalized Oldroyd-B model with only stress tensor diffusion in ℝ²
• Global existence and optimal decay of solutions to the incompressible Oldroyd-B model with only stress tensor dissipation and without damping mechanism
• Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model
• Global well-posedness and inviscid limits of the generalized Oldroyd type models
• Global existence and decay rate of strong solution to incompressible Oldroyd type model equations