Global solutions to the Oldroyd-B model with a class of large initial data

Abstract

Consider a global wellposed problem for the incompressible Oldroyd-B model. It is shown that this set of equations admits a unique global solution provided the initial horizontal velocity $u_0^h$, the product $\om u^d_0$ of the coupling parameter $\om$ and initial the vertical velocity $u_0^d$, and initial symmetric tensor of constrains ${\tau }_0$ are sufficient small in the scaling invariant Besov space $\dot{B}^{\fr{d}{2}-1}_{2,1}\times\dot{B}^{\fr{d}{2}}_{2,1}, d\ge2$. In particular, the result implies the global well-posedness of Oldroyd-B model with large initial vertical velocity $u_0^d$.

24pages. arXiv admin note: text overlap with arXiv:1410.7483

References in corpus (4)

• On 2D Viscoelasticity with Small Strain
• Global solution to the incompressible Oldroyd-B model in hybrid Besov spaces
• Global solutions of two dimensional incompressible viscoelastic flows with discontinuous initial data
• Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter