×

Optimal roughening of convex bodies. (English) Zbl 1261.37020

Summary: A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies \(C_1\) and \(C_2\) such that \(C_1\subset C_2\subset \mathbb{R}^3\) and \(\partial C_1\cap \partial C_2=\emptyset\), minimize the resistance in the class of connected bodies \(B\) such that \(C_1\subset B\subset C_2\). We prove that the infimum of resistance is zero; that is, there exist “almost perfectly streamlined” bodies.

MSC:

37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
49Q10 Optimization of shapes other than minimal surfaces
PDFBibTeX XMLCite
Full Text: DOI