Water and air behave in a similar way and their flow can be described in a very accurate
way by the Navier–Stokes equations. Others fluids behave differently: they cannot be …

The small data global well-posedness in Sobolev setting for the incompressible Oldroyd-B
equations with only velocity dissipation (namely there is no damping or dissipation of stress …

One of the most classical closures approximation of the FENE model of polymeric flows is
the one proposed by Peterlin, namely the FENE-P model. We prove global existence of …

In this paper, we revise Maxwell's constitutive relation and formulate a system of first-order
partial differential equations with two parameters for compressible viscoelastic fluid flows …

We consider smooth solutions to a relaxed Euler system with Oldroyd-type constitutive laws.
This system is derived from the one-dimensional compressible full Navier-Stokes equations …

Viscoelastic flows of polymer solutions in complex geometries can generate a strong
localization of stress within small regions of the fluid and the formation of birefringent …

There have been substantial recent developments on the stability problem concerning the
Oldroyd-B model of the incompressible non-Newtonian fluids, especially when the system …

We consider a model of one dimensional isentropic compressible Navier–Stokes equations
for which the classical Newtonian flow is replaced by a Maxwell flow. We establish the …

A core-annular flow of an Oldroyd-B fluid surrounded by a lubricating Bingham fluid is
studied using energy stability methods. We consider base flows for which the lubricating …

This article addresses the low Weissenberg asymptotic analysis (Newtonian limit) of some
macroscopic models of viscoelastic fluid flows in the framework of global weak solutions. We …