2021/10/16 by Zhi Chen, Chen, Zhi, Weikui Ye +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2110.09517
openalex publication_date 2021/10/16 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28
In this paper, we consider the 2-dimensional non-viscous Oldroyd-B model. In the case of the ratio equal 1~(α=0), it is a difficult case since the velocity field u(t,x) is no longer decay. Fortunately, by observing the exponential decay of the stress tensor τ(t,x), we succeeded in proving the global existence for this system with some large initial data. Moreover, we give an unsteady result: when the ratio is close to 1~(a→ 0), the system is not steady for large time. This implies an interesting physical phenomenon that the term a\mathbbDu is a bridge between the transformation of kinetic energy u and elastic potential energy τ, but this process is transient for large time, which leads the instability.