Global Existence of Classical Solutions for the Two-Dimensional Oldroyd Model via the Incompressible Limit

A thermodynamically compatible rate type fluid to describe the response of asphalt

“…Various interesting results concerning the local-well posedness of the initial-boundary value problem for the Oldroyd type fluids have been recently established in several studies, see [17,14,9]. In two dimensions, the local in time existence of smooth solutions is established in [16] or [15]. We refer the interested reader to the above mentioned studies or to an earlier paper [8] for details and further references.…”

Global Solutions to the Oldroyd-B Model with a Class of Large Initial Data

“…Besides, we would like to mention that Constantin and Kliegl [9] proved the global regularity of solutions in two dimensional case for the Oldroyd-B fluids with diffusive stress. An approach based on Lagrangian particle dynamics can be found in [19,20,21,23,24,25,30,32].…”

Global wellposedness to the generalized Oldroyd type models in R3

“…An improvement of the Chemin-Masmoudi blow-up criterion was presented recently by Lei et al [12]. Much work has been limited to global existence of weak solutions and global well-posedness for smooth solutions to Oldroyd model and related models ( [2], [5], [7], [9], [10], [13], [14], [15], [16], [17], [19], [21], [26], [27], [28]). …”