Seminar talk, 14 February 2024
Speaker: Valentin Lychagin
Title: On flows and filtration in the presence of thermodynamic processes: generalized Navier-Stokes equations
We plan to present a generalization of the Navier-Stokes equations that describes the flows of homogeneous multicomponent media in the presence of various thermodynamic processes, especially chemical reactions. To achieve this, we discuss the classical thermodynamics of homogeneous multicomponent media and related thermodynamic processes (especially chemical reactions) from the contact geometry perspective.
It makes it possible to work with thermodynamic processes as contact vector fields on a contact manifold and easily include in the standard scheme of continuous mechanics. At the end, we outline methods of solving resulting equations and discuss possible singularities arising in solutions.