Global Regularity and instability for the incompressible nonviscous OldroydB model
Abstract
In this paper, we consider the 2dimensional nonviscous OldroydB model. In the case of the ratio equal 1~($\alpha=0$), 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 $\tau(t,x)$, 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~($a\rightarrow 0$), the system is not steady for large time. This implies an interesting physical phenomenon that the term $a\mathbb{D}u$ is a bridge between the transformation of kinetic energy $u$ and elastic potential energy $\tau$, but this process is transient for large time, which leads the instability.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09517
 Bibcode:
 2021arXiv211009517C
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 OldroydB model