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We consider Newton's problem of minimal resistance, in particular we addressthe problem arising in the limit if the height goes to infinity. We establishexistence of solutions and lack radial symmetry of solutions. Moreover, we showthat certain conical parts contained in the boundary of a convex body inhibitthe optimality in the classical Newton's problem with finite height. Thisresult is applied to certain bodies considered in the literature, which areconjectured to be optimal for the classical Newton's problem, and we show thatthey are not.

Non-optimality of conical parts for Newton's problem of minimal resistance in the class of convex bodies and the limiting case of infinite height