Research Fellows Directory
Dr Aneta Wroblewska-Kaminska
Imperial College London
The aim of our research is to provide the mathematical analysis of nonlinear partial differential equations of fluid mechanics and their solutions in order to have better understanding of some complex fluids flows.
Particularly, we are interested in hydrodynamic systems for interacting particles where attraction is taken into account by nonlocal forces derived from a potential and repulsion is introduced by local pressure arise in swarming modelling. We are investigating the global existence of solutions for these hydrodynamic models and long time behaviour.
We are investigating also in a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system. The velocity is supposed to fulfil the full-slip boundary condition and we assume that the fluid is thermally isolated. Our existence of solutions studies nontrivially extend the results on the barotropic case. Such model may be used to describe the motion of a piston in a cylinder filled by a viscous heat conducting gas.
Next we are analysing polymeric fluids which viscosity is influenced by behaviour of molecules. Analysis of polymeric liquids can be based on analysis of Navier-Stokes-Fokker-Planck systems which arise from kinetic models for polymer flow. We are interesting in low Mach number analysis of compressible model, what may justify incompressible model used widely in numerical analysis.
We also study the the asymptotic dynamics of the rescaled compressible Navier-Stokes-Fourier system in rotating domain when the speed of sound dominates the characteristic speed of fluid (the Mach number is small) and rotation is fast (Rossby number is smal). This analysis justifies the incompressible model with horizontal velocity field - so the model which is less expensive for numerical simulations of atmospheric flows.