Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
We prove that there exists a weak solution to a system governing an unsteady flow of a
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
Thermodynamics of viscoelastic rate-type fluids with stress diffusion
We propose thermodynamically consistent models for viscoelastic fluids with a stress
diffusion term. In particular, we derive variants of compressible/incompressible …
diffusion term. In particular, we derive variants of compressible/incompressible …
Quasistatic hypoplasticity at large strains Eulerian
T Roubíček - Journal of Nonlinear Science, 2022 - Springer
The isothermal quasistatic (ie acceleration neglected) hardening-free plasticity at large
strains is considered, based on the standard multiplicative decomposition of the total strain …
strains is considered, based on the standard multiplicative decomposition of the total strain …
Weak-strong uniqueness and energy-variational solutions for a class of viscoelastoplastic fluid models
We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes
the flow in terms of the fluid velocity and a symmetric deviatoric stress tensor. This stress …
the flow in terms of the fluid velocity and a symmetric deviatoric stress tensor. This stress …
Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models
T Roubíček - Acta Mechanica, 2024 - Springer
Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin–Voigt,
Maxwell's, and Jeffreys' types are analysed in linear one-dimensional situations as far as the …
Maxwell's, and Jeffreys' types are analysed in linear one-dimensional situations as far as the …
On the Cauchy problem for a compressible Oldroyd-B model without stress diffusion
S Liu, Y Lu, H Wen - SIAM Journal on Mathematical Analysis, 2021 - SIAM
This article is devoted to the global well-posedness and associated time-decay estimates of
strong solutions for the compressible Oldroyd-B model without stress diffusion in R^3. By …
strong solutions for the compressible Oldroyd-B model without stress diffusion in R^3. By …
Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given
by the fluid velocity and an internal stress tensor that is transported along the flow with the …
by the fluid velocity and an internal stress tensor that is transported along the flow with the …
On a class of compressible viscoelastic rate-type fluids with stress-diffusion
We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids
with stress diffusion. Our approach is based on the concepts used in the nowadays standard …
with stress diffusion. Our approach is based on the concepts used in the nowadays standard …
Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation
In the classical theory of fluid mechanics a linear relationship between the shear stress and
the symmetric velocity gradient tensor is often assumed. Even when a nonlinear relationship …
the symmetric velocity gradient tensor is often assumed. Even when a nonlinear relationship …
Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis
We prove that there exists a~ large-data and global-in-time weak solution to a~ system of
partial differential equations describing an unsteady flow of an incompressible heat …
partial differential equations describing an unsteady flow of an incompressible heat …