Page 541 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 541
PARTIAL DIFFERENTIAL EQUATIONS DESCRIBING FAR-FROM-EQUILIBRIUM
OPEN SYSTEMS (MS-51)
multicomponent fluids in non–equilibrium. If time allows, we shall also discuss recent well–
posedness issues concerning the PDEs for multicomponent incompressible fluids. The talk
relies on joined works with D. Bothe (TU Darmstadt) and W. Dreyer (WIAS Berlin).
Ergodic theory for energetically open fluid systems
Eduard Feireisl, feireisl@math.cas.cz
Czech Academy of Sciences, Czech Republic
We consider global in time (weak) solutions for the complete Navier-Stokes-Fourier system
describing the motion of a compressible, viscous and heat conducting fluid driven by inho-
mogeneous boundary conditions. We show that any globally bounded trajectory generates a
stationary statistical solution. Then the Birkhoff-Khinchin theorem can be applied to show the
validity of the (weak) ergodic hypothesis on the associated omega-limit set.
A semismooth Newton method for implicitly constituted flow
Pablo Alexei Gazca Orozco, alexei.gazca@math.fau.de
FAU Erlangen-Nürnberg, Germany
We propose a semismooth Newton method for non-Newtonian models of incompressible flow
where the constitutive relation between the shear stress and the symmetric velocity gradient is
given implicitly; as a motivating example, we consider the Bingham model for viscoplastic flow.
The proposed method avoids the use of variational inequalities and is based on a particularly
simple regularisation introduced recently by Bulícˇek et al., for which the (weak) convergence
of the approximate stresses is known to hold. The system is analysed at the function space level
and results in mesh-independent behaviour of the nonlinear iterations.
Uniqueness and regularity of flows of non-Newtonian fluids below critical
power-law growth
Petr Kaplicky, kaplicky@karlin.mff.cuni.cz
Charles University, Czech Republic
We deal with flows of non-Newtonian fluids in three-dimensional setting subjected to the ho-
mogeneous Dirichlet boundary condition. We assume the natural monotonicity, coercivity and
growth condition on the Cauchy stress tensor expressed by a power index p.
First we present the results for p ≥ 11/5, namely regularity properties of a solution with
respect to time variable and uniqueness of solutions for nice data.
Second we concentrate on estimates for p < 11/5. We show regularity and uniqueness for
small data and show that the restriction on data explodes if p goes to 11/5.
539
OPEN SYSTEMS (MS-51)
multicomponent fluids in non–equilibrium. If time allows, we shall also discuss recent well–
posedness issues concerning the PDEs for multicomponent incompressible fluids. The talk
relies on joined works with D. Bothe (TU Darmstadt) and W. Dreyer (WIAS Berlin).
Ergodic theory for energetically open fluid systems
Eduard Feireisl, feireisl@math.cas.cz
Czech Academy of Sciences, Czech Republic
We consider global in time (weak) solutions for the complete Navier-Stokes-Fourier system
describing the motion of a compressible, viscous and heat conducting fluid driven by inho-
mogeneous boundary conditions. We show that any globally bounded trajectory generates a
stationary statistical solution. Then the Birkhoff-Khinchin theorem can be applied to show the
validity of the (weak) ergodic hypothesis on the associated omega-limit set.
A semismooth Newton method for implicitly constituted flow
Pablo Alexei Gazca Orozco, alexei.gazca@math.fau.de
FAU Erlangen-Nürnberg, Germany
We propose a semismooth Newton method for non-Newtonian models of incompressible flow
where the constitutive relation between the shear stress and the symmetric velocity gradient is
given implicitly; as a motivating example, we consider the Bingham model for viscoplastic flow.
The proposed method avoids the use of variational inequalities and is based on a particularly
simple regularisation introduced recently by Bulícˇek et al., for which the (weak) convergence
of the approximate stresses is known to hold. The system is analysed at the function space level
and results in mesh-independent behaviour of the nonlinear iterations.
Uniqueness and regularity of flows of non-Newtonian fluids below critical
power-law growth
Petr Kaplicky, kaplicky@karlin.mff.cuni.cz
Charles University, Czech Republic
We deal with flows of non-Newtonian fluids in three-dimensional setting subjected to the ho-
mogeneous Dirichlet boundary condition. We assume the natural monotonicity, coercivity and
growth condition on the Cauchy stress tensor expressed by a power index p.
First we present the results for p ≥ 11/5, namely regularity properties of a solution with
respect to time variable and uniqueness of solutions for nice data.
Second we concentrate on estimates for p < 11/5. We show regularity and uniqueness for
small data and show that the restriction on data explodes if p goes to 11/5.
539
