The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 in lecture room K3. The talk will be given by Miroslav Bulíček. Please see the details below.
Speaker: Miroslav Bulíček
Title: On uniqueness of the flow of incompressible fluids – from Navier–Stokes to Ladyzhenskaya and back to Euler
Abstract: The question of the uniqueness of a (proper) solution to the equations describing the flow of incompressible fluids belongs to the most classical open problems in the analysis of PDE’s. The story started by the work of Leray 90 years ago. As usual during the decades there were many trends in the analysis of the Navier-Stokes and/or the Euler equations and their generalizations – the focus was on the regularity, partial regularity, uniqueness, conditional uniquenes/regularity, existence of measure valued solutions up to recent decade full of the results about the non-uniqueness of a solution implying that our concepts and understanding of the notion of the solution must be revised. We present a certain idea how to change the equations/constitutive laws only for extremely large shear-rates so that the modified Navier-Stokes or Euler equations have unique solution. Moreover, such a modification does not change the solution to the original problem at least on a short time interval. Hence, it can be understood as another concept of a solution with the key advantage – it exists globally in time and it is unique.