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Description

Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

Prof. Eduard Feireisl, Czech Academy of Sciences