Stochastic models of polymeric fluids at small Deborah number

Weak Solutions of a Stochastic Model for Two-Dimensional Second Grade Fluids

“…We refer, for instance, to [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] . Similar investigations for Non-Newtonian fluids have almost not been undertaken except in very few work; we refer, for instance, to [23][24][25] for some computational studies of stochastic models of polymeric fluids. It is worth to note that in the Non-Newtonian case the study of stochastic models is relevant not only for the analytical approach to turbulent flows but also for practical needs related to the physics of the corresponding fluids 2 .…”

A Molecular Kinetic Theory of Inhomogeneous Liquid Crystal Flow and the Small Deborah Number Limit

“…Our purpose is to derive the well-known Ericksen-Leslie equations from systematic asymptotic analysis. Some initial ideas of this work can be found in [9].…”

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

“…Many works have been devoted to the study of fluids at small De number [16,18,25] and it is put in evidence that the behavior of the flow in this case is equivalent to the case of a Newtonian fluid with a proper viscosity. Nevertheless it is also shown (in theoretical and experimental way) that there is a difference in their behaviour.…”

“…This model has been also treated by Balmforth et al [2] so as the numerical approximation of Herschel-Bulkley models, for example in the paper written by Ancey [1]. Some other results related to the approximation of non-Newtonian fluids are based in the resolution of the Navier-Stokes equations together with a rheological model, see for example [25,36]. We also mention the interesting recent paper by Bouchut and Boyaval, see [5], where they propose a reduced model for gravity-driven free-surface flows of shallow-water elastic fluids which is close to ours.…”