Vit Prusa (Univ. Karlova) - Thermodynamics and finite amplitude stability

We show how to exploit the knowledge of the thermodynamic background in the study of nonlinear (finite amplitude) stability of steady solutions to the systems nonlinear partial differential equations governing the motion of continuous medium. In particular, we focus on thermodynamically open systems, that is on the case where the system of interest is allowed to interact with its surroundings, and where one has applications of the proposed approach will be discussed — stability of the incompressible Navier-Stokes-Fourier fluid in a vessel with walls kept at spatially non-uniform temperature, and stability of a steady flow of a viscoelastic rate-type fluid.