Global existence and decay rates of solutions to the Oldroyd-B model with stress tensor diffusion

In this paper, we consider the Oldroyd-B model with stress tensor diffusion in R-d with d > 2. We first establish the global well-posedness of solutions to this model for small initial data (u(0), tau(0)) is an element of (Bp-1 (d /p-1) boolean AND B-p ,1(d /p+1) ) (d)x (B( p, 1 )d/p)(d xd ) with 1 <= p < infinity. Furthermore, under some additional L-2 type conditions on (u(0), tau(0)), but without any more smallness restrictions, we get the L-2 decay rates of all derivatives of (u, tau). It is shown that the velocity u decays as fast as the solution to the corresponding homogeneous linear heat equation, and the symmetry tau decays as fast as Du. In particular, when d = 3 the velocity u admits the decay rate faster than (1 + t)(-3/4) in L-2 (c) 2024 Elsevier Inc. All rights reserved.