(In)stability phenomena in asymptotic models in fluid dynamics

• Applicant: Dr. Christina Lienstromberg
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545145736

The objective of the network project on (in)stability phenomena in asymptotic models in fluid dynamics lies in building bridges between communities working on thin-film equations on the one hand and water-wave model equations on the other hand. The underlying models are the Navier–Stokes system, respectively the Euler equations. As asymptotic limits of those, the topics of the network project range from the study of thin-film flows in various geometries, such as inclined planes or rotating cylinders, to water waves in the ocean. It is the purpose of this scientific network to tackle these questions within a cooperation of experts and young scientists from four involved institutions at the universities of Bonn, Lund (Sweden), Saarbrücken, and Stuttgart. Three aspects constitute the focus of the network: The first aspect is on the derivation and validation of the governing model equations as asymptotic limit equations from the Navier-Stokes system, respectively the Euler equations. With methods from nonlinear analysis we study different solution concepts for the respective model equations, such as existence and uniqueness of classical strong solutions and globally in time existing weak solutions. Particular attention will be turned to travelling waves as special solutions of the respective equations. The third aspect is on understanding stability and instability phenomena, depending on involved physical parameters such as gravity and surface tension. These questions will be addressed for the following fluid mechanical problems: (A) Stability of thin-film flows on inclined planes, (B) Rimming flows, (C) Transverse (in)stabilities in water-wave model equations. The strength of the project lies in the diversity of the network with respect to the scientific background (thin-film problems and water-wave model equations) and with respect to the different career stages of the involved researchers. This diversity allows us to profit from the different expertise and approaches of the network members and thus to create synergy effects for building new collaborations and for giving young researchers the opportunity to enter in a very active and international network. Due to the change of Christina Lienstromberg from Bonn to Stuttgart a new group, led by Christina Lienstromberg, Wolf-Patrick Düll, and Guido Schneider, was formed working on the above topics. Their expertise is complemented and supplemented by the groups led by Juan J. L. Velázquez in Bonn, Mark Groves in Saarbrücken as well as Gabriele Brüll and Erik Wahlén in Lund. There is already a number of previous and ongoing collaborations between these groups, as well as an ongoing regular joint online-seminar. This allows us to have joint PhD projects with advisors from the four universities and embeds young researchers into an international network.

• DFG Programme: Scientific Networks