Novel mathematical models in biofluid dynamics

Biological fluids possess complex rheological properties, and experimental studied of their behavior revealed inconsistency with mathematical models of classical viscous and viscoelastic fluids. In the talk a brief review of novel discrete and continuous models and problem formulations will be given. Among them are

1) Multidimensional 3d+2d+1d+0d fluid dynamics models in rigid and compliant boundaries;

2) Flows of nanofluids in the micro and nanochannels described by the Navier-Stokes equations with first/second order slip velocity and temperature jump boundary conditions;

3) Continual models of collective dynamics (traffic flows, crowd behavior, schools of fish, flocks of birds, etc.) with slip boundary conditions and ‘social forces’.

The well-posedness of the formulated problems will be discussed, and the corresponding examples of fluids and flows will be given.