The Global Existence of Small Solutions to the Incompressible Viscoelastic Fluid System in 2 and 3 Space Dimensions

Abstract

In this article, we study the Cauchy problem of the viscoelastic fluid system of Oldroyd model in space dimension greater than 1. In particular, we prove that if the smooth solution (U,v) to this system blows up at some finite time T*, then it is necessary that Furthermore, we prove the global existence of smooth solutions to this system provided that initial data is sufficiently close to the equilibrium state.