Page 501 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 501
MATHEMATICAL ANALYSIS: THE INTERACTION OF FLUIDS/ VISCOELASTIC
MATERIALS AND SOLIDS (MS-36)
Dynamics of Hibler’s sea-ice model
Karoline Disser, karoline.disser@gmail.com
Universität Kassel, Germany
Coauthors: Felix Brandt, Robert Haller-Dintelmann, Matthias Hieber
Sea ice is a material with a complex mechanical and thermodynamical behaviour. Freezing
sea water forms a composite of pure ice, liquid brine, air pockets and solid salt. The details
of this formation depend on the laminar or turbulent environmental conditions. The governing
equations of large-scale sea ice dynamics that form the basis of many sea ice models in climate
science were suggested in a seminal paper by Hibler in 1979. We show that Hibler’s sea ice
model that couples a 2D-velocity and two parameters for thickness and compactness of sea ice
based on viscous-plastic rheology is locally strongly well-posed and globally strongly well-
posed for initial data close to constant equilibria.
Regularity for the 3D evolution Navier-Stokes equations under Navier
boundary conditions in some Lipschitz domains
Alessio Falocchi, alessio.falocchi@polito.it
Politecnico di Torino, Italy
Coauthor: Filippo Gazzola
For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the
uniqueness of a solution is related to the existence of a regular solution. They may be obtained
under suitable assumptions on the data and smoothness assumptions on the domain (at least
C2). With a symmetrization technique, we prove these results in the case of Navier boundary
conditions in a wide class of merely Lipschitz domains of physical interest, that we call sectors.
Regularity of a weak solution to a linear fluid-composite structure
interaction problem
Marija Galic´, marijag5555@gmail.com
Faculty of Science, University of Zagreb, Croatia
We deal with the regularity of a weak solution to the fluid-composite structure interaction prob-
lem. The problem describes a linear fluid-structure interaction between an incompressible, vis-
cous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like
elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and
dynamic boundary coupling conditions describing continuity of velocity and balance of contact
forces at the fluid-structure interface. It has been shown that there exists a weak solution to the
described problem. By using the standard techniques from the analysis of partial differential
equations, we prove that such weak solution possesses an additional regularity in both time and
space variables.
499
MATERIALS AND SOLIDS (MS-36)
Dynamics of Hibler’s sea-ice model
Karoline Disser, karoline.disser@gmail.com
Universität Kassel, Germany
Coauthors: Felix Brandt, Robert Haller-Dintelmann, Matthias Hieber
Sea ice is a material with a complex mechanical and thermodynamical behaviour. Freezing
sea water forms a composite of pure ice, liquid brine, air pockets and solid salt. The details
of this formation depend on the laminar or turbulent environmental conditions. The governing
equations of large-scale sea ice dynamics that form the basis of many sea ice models in climate
science were suggested in a seminal paper by Hibler in 1979. We show that Hibler’s sea ice
model that couples a 2D-velocity and two parameters for thickness and compactness of sea ice
based on viscous-plastic rheology is locally strongly well-posed and globally strongly well-
posed for initial data close to constant equilibria.
Regularity for the 3D evolution Navier-Stokes equations under Navier
boundary conditions in some Lipschitz domains
Alessio Falocchi, alessio.falocchi@polito.it
Politecnico di Torino, Italy
Coauthor: Filippo Gazzola
For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the
uniqueness of a solution is related to the existence of a regular solution. They may be obtained
under suitable assumptions on the data and smoothness assumptions on the domain (at least
C2). With a symmetrization technique, we prove these results in the case of Navier boundary
conditions in a wide class of merely Lipschitz domains of physical interest, that we call sectors.
Regularity of a weak solution to a linear fluid-composite structure
interaction problem
Marija Galic´, marijag5555@gmail.com
Faculty of Science, University of Zagreb, Croatia
We deal with the regularity of a weak solution to the fluid-composite structure interaction prob-
lem. The problem describes a linear fluid-structure interaction between an incompressible, vis-
cous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like
elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and
dynamic boundary coupling conditions describing continuity of velocity and balance of contact
forces at the fluid-structure interface. It has been shown that there exists a weak solution to the
described problem. By using the standard techniques from the analysis of partial differential
equations, we prove that such weak solution possesses an additional regularity in both time and
space variables.
499
