Zusammenfassung für den Vortrag am 17.02.2020 (11:00 Uhr)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Lukas Geuter (TU Berlin)
Analysis of a model for dynamics in microswimmer suspensions
In [Reinken et al., 2018], the authors derived a fourth-order continuum theory capable of reproducing mesoscale turbulence in a three-dimensional suspension of microswimmers. This is in some way a refinement of a phenomenological model proposed in [Wensink et al., 2012], that also describes an active fluid consisting of polar moving active particles like, e.g., self-propelling bacteria, suspendend in a fluid. The novelty of the former approach is, that it is capable of distinguishing between the orientation of the particles and the dynamics of the surrounding fluid.
In this talk, we study the mathematical properties of this system, in particular the global existence and weak-strong uniqueness of weak solutions. The latter is shown via the relative energy approach which is then applied to further examine the connection to the phenomenological model, for which strong solutions are available, as was shown in [Zanger et al., 2016].