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Article: Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow
Title | Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow |
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Authors | |
Keywords | BKK theory fixed equilibrium point vortex polynomial system |
Issue Date | 2014 |
Citation | Nonlinearity, 2014, v. 27, p. 2445-2463 How to Cite? |
Abstract | For a dynamic system consisting of n point vortices in an ideal plane fluid with a steady, incompressible and irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under this new definition, if the complex polynomial w that determines the aforesaid background flow is non-constant, we have found an attainable generic upper bound $\frac{(m+n-1)!}{(m-1)!\,n_1!\cdots n_{i_0}!}$ for the number of fixed equilibrium configurations. Here, m = deg w, i0 is the number of species, and each ni is the number of vortices in a species. We transform the rational function system arising from fixed equilibria into a polynomial system, whose form is good enough to apply the BKK theory (named after Bernshtein (1975 Funct. Anal. Appl. 9 183–5), Khovanskii (1978 Funct. Anal. Appl. 12 38–46) and Kushnirenko (1976 Funct. Anal. Appl. 10 233–5)) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem or the BKK root count by Li and Wang (1996 Math. Comput. 65 1477–84). |
Persistent Identifier | http://hdl.handle.net/10722/202989 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 1.357 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | CHEUNG, PL | en_US |
dc.contributor.author | Ng, TW | en_US |
dc.date.accessioned | 2014-09-19T11:06:55Z | - |
dc.date.available | 2014-09-19T11:06:55Z | - |
dc.date.issued | 2014 | en_US |
dc.identifier.citation | Nonlinearity, 2014, v. 27, p. 2445-2463 | en_US |
dc.identifier.issn | 0951-7715 | - |
dc.identifier.uri | http://hdl.handle.net/10722/202989 | - |
dc.description.abstract | For a dynamic system consisting of n point vortices in an ideal plane fluid with a steady, incompressible and irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under this new definition, if the complex polynomial w that determines the aforesaid background flow is non-constant, we have found an attainable generic upper bound $\frac{(m+n-1)!}{(m-1)!\,n_1!\cdots n_{i_0}!}$ for the number of fixed equilibrium configurations. Here, m = deg w, i0 is the number of species, and each ni is the number of vortices in a species. We transform the rational function system arising from fixed equilibria into a polynomial system, whose form is good enough to apply the BKK theory (named after Bernshtein (1975 Funct. Anal. Appl. 9 183–5), Khovanskii (1978 Funct. Anal. Appl. 12 38–46) and Kushnirenko (1976 Funct. Anal. Appl. 10 233–5)) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem or the BKK root count by Li and Wang (1996 Math. Comput. 65 1477–84). | en_US |
dc.language | eng | en_US |
dc.relation.ispartof | Nonlinearity | en_US |
dc.subject | BKK theory | - |
dc.subject | fixed equilibrium | - |
dc.subject | point vortex | - |
dc.subject | polynomial system | - |
dc.title | Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow | en_US |
dc.type | Article | en_US |
dc.identifier.email | Ng, TW: ngtw@hku.hk | en_US |
dc.identifier.authority | Ng, TW=rp00768 | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1088/0951-7715/27/10/2445 | en_US |
dc.identifier.scopus | eid_2-s2.0-84907246483 | - |
dc.identifier.hkuros | 239026 | en_US |
dc.identifier.volume | 27 | en_US |
dc.identifier.spage | 2445 | en_US |
dc.identifier.epage | 2463 | en_US |
dc.identifier.eissn | 1361-6544 | - |
dc.identifier.isi | WOS:000342751000002 | - |
dc.identifier.issnl | 0951-7715 | - |