Page 543 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 543
PARTIAL DIFFERENTIAL EQUATIONS DESCRIBING FAR-FROM-EQUILIBRIUM
OPEN SYSTEMS (MS-51)
Thermodynamics of viscoelastic rate-type fluids and its implications for
stability analysis
Vít Pru˚ša, prusv@karlin.mff.cuni.cz
Charles University, Czech Republic
We introduce a thermodynamic basis for some non-Newtonian fluids, namely we explicitly
characterise energy storage and entropy production mechanisms that lead to the frequently
used viscoelastic rate-type models such as the Oldroyd-B model, the Giesekus model, the
Phan-Thien–Tanner model, the Johnson–Segalman model, the Bautista–Manero–Puig model
and their diffusive variants. Knowing the thermodynamical basis of the models, we show how
this knowledge can be used in nonlinear (finite amplitude) stability analysis of steady flows of
these fluids.
The Maxwell-Stefan system, its gradient flow structure, and the problem
of uniqueness of weak solutions
Athanasios Tzavaras, athanasios.tzavaras@kaust.edu.sa
King Abdullah University of Science and Technology, Saudi Arabia
We consider the Maxwell-Stefan system and discuss the following items: (i) How it emerges in
the high-friction limit of multi-component Euler flows. (ii) The question of uniqueness of weak
solutions for the Maxwell-Stefan model. (iii) The construction of numerical schemes for the
Maxwell-Stefan system associated with the minimization of frictional dissipation.
(based on joint works with Xiaokai Huo, Ansgar Jüngel, Hailiang Liu and Shuaikun Wang)
Hydrodynamic stability for the dynamic slip
Michael Zelina, zelina@karlin.mff.cuni.cz
Charles University, Czech Republic
We consider the incompressible Navier-Stokes equation with the dynamic slip boundary condi-
tion. Our first goal is to prove the so-called linearization principle in the class of weak solutions
satisfying the energy inequality. By this we mean that if the spectrum of certain operator has
only positive real parts, then the stationary solution u∗ of the Navier-Stokes equation is sta-
ble with respect to sufficiently small initial perturbations. We deal further with two explicit
geometries, namely with either two infinite parallel planes or two concentric cylinders, where
the solution u∗ corresponds either to Couette/Poiseuille or Taylor-Couette flow. We eventu-
ally compare our results with well-known analogue results in the case of Dirchlet boundary
condition.
541
OPEN SYSTEMS (MS-51)
Thermodynamics of viscoelastic rate-type fluids and its implications for
stability analysis
Vít Pru˚ša, prusv@karlin.mff.cuni.cz
Charles University, Czech Republic
We introduce a thermodynamic basis for some non-Newtonian fluids, namely we explicitly
characterise energy storage and entropy production mechanisms that lead to the frequently
used viscoelastic rate-type models such as the Oldroyd-B model, the Giesekus model, the
Phan-Thien–Tanner model, the Johnson–Segalman model, the Bautista–Manero–Puig model
and their diffusive variants. Knowing the thermodynamical basis of the models, we show how
this knowledge can be used in nonlinear (finite amplitude) stability analysis of steady flows of
these fluids.
The Maxwell-Stefan system, its gradient flow structure, and the problem
of uniqueness of weak solutions
Athanasios Tzavaras, athanasios.tzavaras@kaust.edu.sa
King Abdullah University of Science and Technology, Saudi Arabia
We consider the Maxwell-Stefan system and discuss the following items: (i) How it emerges in
the high-friction limit of multi-component Euler flows. (ii) The question of uniqueness of weak
solutions for the Maxwell-Stefan model. (iii) The construction of numerical schemes for the
Maxwell-Stefan system associated with the minimization of frictional dissipation.
(based on joint works with Xiaokai Huo, Ansgar Jüngel, Hailiang Liu and Shuaikun Wang)
Hydrodynamic stability for the dynamic slip
Michael Zelina, zelina@karlin.mff.cuni.cz
Charles University, Czech Republic
We consider the incompressible Navier-Stokes equation with the dynamic slip boundary condi-
tion. Our first goal is to prove the so-called linearization principle in the class of weak solutions
satisfying the energy inequality. By this we mean that if the spectrum of certain operator has
only positive real parts, then the stationary solution u∗ of the Navier-Stokes equation is sta-
ble with respect to sufficiently small initial perturbations. We deal further with two explicit
geometries, namely with either two infinite parallel planes or two concentric cylinders, where
the solution u∗ corresponds either to Couette/Poiseuille or Taylor-Couette flow. We eventu-
ally compare our results with well-known analogue results in the case of Dirchlet boundary
condition.
541
