Newton’s problem of least resistance for convex bodies

Speaker(s)

Alexander Plakhov

Affiliation

University of Aveiro, Portugal

Language of the talk

English

Date

May 14, 2025, 12:30 p.m.

Room

room 3170

Seminar

Seminarium Zakładu Równań i Analizy

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Isaac Newton (1687) posed the problem of finding the convex axisymmetric body with smallest
aerodynamic drag when moving in a highly rarefied medium. Thus, he was looking for the
optimal curve which is the generatrix of the body. In 1993, a similar problem was formulated in a
wider class of convex (not necessarily symmetric) bodies. This task proved to be much more
difficult: it is about finding the optimal surface. This problem still remains open. The talk will
provide an overview of recent results and methods used. А special attention will be paid to the
following statement: an optimal body is the closure of the convex hull of the set of its singular
points. In other words, the surface of an optimal body outside the closure of its singular set can
be foliated by line segments. The proof is based on a method of small variation of convex
bodies called nose stretching.

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