Seminar on Qualitative Theory of Differential Equations - Danica Basarić (18.11.2021)
Thursday 18.11.2021 at 14:00, Lecture room M 223
By: Pavol Quittner
Danica Basarić (Institute of Mathematics, Czech Academy of Sciences ):
Semiflow Selections in Fluid Dynamics
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.