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 Comment on "functions and domains having minimal resistance under a single-impact assumption"
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6316

title: Comment on "functions and domains having minimal resistance under a single-impact assumption"
authors: Plakhov, A.
keywords: Newton's problem
Surface of minimal resistance
Calculus of variations
Least value
Parallel flows
Point particle
Specific resistances
Aerospace vehicles
Impact resistance
Parallel flow
Surface resistance
issue date: 2009
abstract: Recently Comte and Lachand-Robert [SIAM J. Math. Anal., 34 (2002), pp. 101-120] stated a very interesting and actual problem of minimizing mean specific resistance of infinite surfaces in a parallel flow of noninteracting point particles. They also constructed surfaces having resistance 0.593 and proved that they are minimizers. Unfortunately, their proof is incorrect. In this comment we provide a counterexample showing that the least value of resistance is not attained and is less than 0.581 (but greater than or equal to 0.5). Therefore, the problem remains open. Copyright by SIAM.
URI: http://hdl.handle.net/10773/6316
ISSN: 0036-1410
publisher version/DOI: http://dx.doi.org/10.1137/09075439X
source: SIAM Journal on Mathematical Analysis
appears in collectionsCIDMA - Artigos

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