Global solutions to the $n$-dimensional incompressible Oldroyd-B model without damping mechanism

Abstract

The present work is dedicated to the global solutions to the incompressible Oldroyd-B model without damping on the stress tensor in $\mathbb{R}^n(n=2,3)$. This result allows to construct global solutions for a class of highly oscillating initial velocity. The proof uses the special structure of the system. Moreover, our theorem extends the previous result by Zhu [19] and covers the recent result by Chen and Hao [4].