Page 538 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 538
PARTIAL DIFFERENTIAL EQUATIONS DESCRIBING FAR-FROM-EQUILIBRIUM
OPEN SYSTEMS (MS-51)
On the stability of generalized viscous heat-conducting incompressible
fluids with non-homogeneous boundary temperature
Anna Abbatiello, anna.abbatiello@uniroma1.it
“Sapienza" Università di Roma, Italy
The motions of a generalized viscous heat-conducting incompressible fluid are governed by
the non-standard Navier-Stokes-Fourier system where the non-linear viscosity depends on the
shear-rate and the temperature. Assuming the fluid occupies a mechanically isolated container
with a spatially non-homogeneous temperature boundary condition, the issue of stability con-
cerns the investigation of the long-time behaviour of the fluid, which is expected to reach a
steady state. The steady state is the state where the velocity field vanishes and the steady tem-
perature field satisfies the steady heat equation with non-homogeneous boundary temperature.
The aim of our study is to develop a rigorous stability analysis in the setting of weak solutions
satisfying the equation for the entropy production. This is a joint work with Miroslav Bulícˇek
and Petr Kaplický.
Bifurcations, pattern formation and synchronization in a few RD systems
and networks of RD systems
Benjamin Ambrosio, benjamin.ambrosio@univ-lehavre.fr
Le Havre Normandie University, France
In this talk, I will provide theoretical and numerical insights in bifurcation phenomena and
pattern formation occurring in some nonlinear reaction diffusion systems. I will also discuss
the synchronization phenomenon in networks of reaction-diffusion systems. This includes the
synchronization of patterns.
A quantitative approach to the Navier-Stokes equations
Tobias Barker, tobiasbarker5@gmail.com
University of Warwick, United Kingdom
Coauthor: Christophe Prange
It remains open as to whether or not the 3D Navier-Stokes equations lose smoothness (‘blow-
up’) in finite time. Very recently, Terence Tao used a new quantitative approach to infer that cer-
tain ’slightly supercritical’ quantities for the Navier-Stokes equations must become unbounded
near a potential blow-up time. In this talk I’ll discuss a new strategy for proving quantitative
bounds for the Navier-Stokes equations, as well as applications to behaviours of potentially
singular solutions.
536
OPEN SYSTEMS (MS-51)
On the stability of generalized viscous heat-conducting incompressible
fluids with non-homogeneous boundary temperature
Anna Abbatiello, anna.abbatiello@uniroma1.it
“Sapienza" Università di Roma, Italy
The motions of a generalized viscous heat-conducting incompressible fluid are governed by
the non-standard Navier-Stokes-Fourier system where the non-linear viscosity depends on the
shear-rate and the temperature. Assuming the fluid occupies a mechanically isolated container
with a spatially non-homogeneous temperature boundary condition, the issue of stability con-
cerns the investigation of the long-time behaviour of the fluid, which is expected to reach a
steady state. The steady state is the state where the velocity field vanishes and the steady tem-
perature field satisfies the steady heat equation with non-homogeneous boundary temperature.
The aim of our study is to develop a rigorous stability analysis in the setting of weak solutions
satisfying the equation for the entropy production. This is a joint work with Miroslav Bulícˇek
and Petr Kaplický.
Bifurcations, pattern formation and synchronization in a few RD systems
and networks of RD systems
Benjamin Ambrosio, benjamin.ambrosio@univ-lehavre.fr
Le Havre Normandie University, France
In this talk, I will provide theoretical and numerical insights in bifurcation phenomena and
pattern formation occurring in some nonlinear reaction diffusion systems. I will also discuss
the synchronization phenomenon in networks of reaction-diffusion systems. This includes the
synchronization of patterns.
A quantitative approach to the Navier-Stokes equations
Tobias Barker, tobiasbarker5@gmail.com
University of Warwick, United Kingdom
Coauthor: Christophe Prange
It remains open as to whether or not the 3D Navier-Stokes equations lose smoothness (‘blow-
up’) in finite time. Very recently, Terence Tao used a new quantitative approach to infer that cer-
tain ’slightly supercritical’ quantities for the Navier-Stokes equations must become unbounded
near a potential blow-up time. In this talk I’ll discuss a new strategy for proving quantitative
bounds for the Navier-Stokes equations, as well as applications to behaviours of potentially
singular solutions.
536
