Links for fulltext
(May Require Subscription)
 Publisher Website: 10.1088/09517715/27/10/2445
 WOS: WOS:000342751000002
Supplementary

Citations:
 Web of Science: 0
 Appears in Collections:
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 

Authors  
Issue Date  2014 
Citation  Nonlinearity, 2014, v. 27, p. 24452463 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 nonconstant, we have found an attainable generic upper bound $\frac{(m+n1)!}{(m1)!\,n_1!\cdots n_{i_0}!}$ 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 
ISI Accession Number ID 
DC Field  Value  Language 

dc.contributor.author  CHEUNG, PL  en_US 
dc.contributor.author  Ng, TW  en_US 
dc.date.accessioned  20140919T11:06:55Z   
dc.date.available  20140919T11:06:55Z   
dc.date.issued  2014  en_US 
dc.identifier.citation  Nonlinearity, 2014, v. 27, p. 24452463  en_US 
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 nonconstant, we have found an attainable generic upper bound $\frac{(m+n1)!}{(m1)!\,n_1!\cdots n_{i_0}!}$ 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.rights  Creative Commons: Attribution 3.0 Hong Kong License   
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  10.1088/09517715/27/10/2445  en_US 
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.isi  WOS:000342751000002   