hidden - assigned and confirmed by the Study Dept.
Date of registration:
27.09.2018
Date of assignment:
27.09.2018
Confirmed by Study dept. on:
03.10.2023
Guidelines
The subject of the thesis would be a fluid interacting with a flexible membrane, that is described as a part of a variable boundary. As is common in Navier Stokes, it is possible to show the existence of strong unique solutions in two space dimensions. The first aim is to establish the same, for the setting, when a variable boundary is involved. The second aim is to improve the known results for weak solutions to situations, where the fluid can have more impact on the membrane sitting on a part of the boundary. This includes the challenge of allowing tangential forces to act on the membrane. Here the frame of existence has to be analyzed carefully, since self intersections must be excluded and should not happen if not big forces are involved.
References
D. Lengeler, M. Růžička: "Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell" , Arch. Ration. Mech. Anal. 211 (2014), no. 1, 205-255.
B. Muha, S. Canic: "Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls", Arch. Ration. Mech. Anal. Vol. 207 (3), 919-968, 2013,
- assigned and confirmed by the Study Dept.