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http://hdl.handle.net/10773/6316| Title: | Comment on "functions and domains having minimal resistance under a single-impact assumption" |
| Author: | 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. |
| Peer review: | yes |
| URI: | http://hdl.handle.net/10773/6316 |
| DOI: | 10.1137/09075439X |
| ISSN: | 0036-1410 |
| Appears in Collections: | CIDMA - Artigos |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2009 SIMA comment.pdf | 190.87 kB | Adobe PDF | View/Open |
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