Seminar 18.11.2021: Danica Basaric

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Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 18.11.2021 at 14:00 Lecture room M-223

Danica Basarić (Institute of Mathematics, Czech Academy of Sciences):
Semiflow Selections in Fluid Dynamics

Abstract:
Well-posedness of systems describing the motion of fluids in the class
of strong and weak solutions represents one of the most challenging problems
in the modern theory of partial differential equations.
To handle the problem of uniqueness, one possible way is to perform
a semiflow selection, identifying, among all the solutions emanating
from the same initial data, the one satisfying the semigroup property.
We study under which assumptions it is possible to guarantee the existence
of a semiflow selection, choosing the Skorokhod space of càglàd functions
as trajectory space. Subsequently, we apply this abstract machinery
to systems arising in fluid dynamics, including the compressible
Navier-Stokes system and models describing general non-Newtonian fluids.