4,441 research outputs found
PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion
We establish the long-time existence of large-data weak solutions to a system
of nonlinear partial differential equations. The system of interest governs the
motion of non-Newtonian fluids described by a simplified viscoelastic rate-type
model with a stress-diffusion term. The simplified model shares many
qualitative features with more complex viscoelastic rate-type models that are
frequently used in the modeling of fluids with complicated microstructure. As
such, the simplified model provides important preliminary insight into the
mathematical properties of these more complex and practically relevant models
of non-Newtonian fluids. The simplified model that is analyzed from the
mathematical perspective is shown to be thermodynamically consistent, and we
extensively comment on the interplay between the thermodynamical background of
the model and the mathematical analysis of the corresponding
initial-boundary-value problem
Weak Solutions for a Non-Newtonian Diffuse Interface Model with Different Densities
We consider weak solutions for a diffuse interface model of two non-Newtonian
viscous, incompressible fluids of power-law type in the case of different
densities in a bounded, sufficiently smooth domain. This leads to a coupled
system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard
equation. For the Cahn-Hilliard part a smooth free energy density and a
constant, positive mobility is assumed. Using the -truncation method
we prove existence of weak solutions for a power-law exponent
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