Jarníkovská přednáška profesora Málka

Josef Málek je profesorem MFF UK, ředitelem Nečasova centra pro matematické modelování a vedoucím Oddělení matematického modelování Matematického ústavu UK. Jeho výzkum klade důraz na interakce mezi modelováním, analýzou, vědeckými výpočty a experimenty. Přispěl zejména k analýze nelineárních parciálních diferenciálních rovnic v mechanice nenewtonských tekutin a k rozvoji teorie mechaniky tekutin a pevných látek a teorie směsí.

Abstrakt přednášky:

A century ago mathematicians and theoretical physicists changed the viewpoint regarding the concept of solution to partial differential equations in general, and to the incompressible Navier-Stokes equations in particular. Instead of interpreting the solution to a partial differential equation as a complicated mapping between two sets of variables, they began to view the solution as a point in a suitable infinite-dimensional space. In a landmark paper published in 1934, based on connections between mathematical approaches and the physical underpinnings of the problem, Jean Leray developed a robust mathematical framework for the analysis of solutions to the Navier-Stokes equations in the aforementioned sense. Stimulated by Leray’s foundational work, a similar analysis has been since then completed for various systems of nonlinear partial differential equations describing mechanical, thermal, and chemical processes in various materials. In the talk, we briefly introduce non-Newtonian fluids, that is the fluids that cannot be described by the Navier-Stokes equations, and then we discuss recent results regarding the mathematical analysis of the partial differential equations governing the motion of these fluids.

OPMK, foto Tomáš Rubín