Optimal Roughening of Convex Bodies

Plakhov, Alexander

Canadian journal of mathematics, Tome 64 (2012) no. 5, pp. 1058-1074

Résumé

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}}\,=\,\varnothing $ , 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.

Détail

DOI : 10.4153/CJM-2011-070-9

Mots-clés : 37D50, 49Q10, billiards, shape optimization, problems of minimal resistance, Newtonian aerodynamics, rough surface