VortexCalculations

Mathematica notebook VortexCalculations.nb: Finiteness of stationary configurations of the four-vortex problem. We show that the number of relative equilibria, equilibria, and rigidly translating configurations in the problem of four point vortices is finite. The proof is based on symbolic and exact integer computations which are carried out by computer. We also provide upper bounds for these classes of stationary configurations.


References in zbMATH (referenced in 14 articles , 1 standard article )

Showing results 1 to 14 of 14.
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  1. Wang, Qun: Relative periodic solutions of the N-vortex problem via the variational method (2019)
  2. Menezes, Brian; Roberts, Gareth E.: Existence and stability of four-vortex collinear relative equilibria with three equal vorticities (2018)
  3. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  4. Tsai, Ya-Lun: Numbers of relative equilibria in the planar four-vortex problem: some special cases (2017)
  5. Sommars, Jeff; Verschelde, Jan: Pruning algorithms for pretropisms of Newton polytopes (2016)
  6. Chen, Tianran; Li, Tien-Yien: Homotopy continuation method for solving systems of nonlinear and polynomial equations (2015)
  7. Pérez-Chavela, E.; Santoprete, Manuele; Tamayo, Claudia: Symmetric relative equilibria in the four-vortex problem with three equal vorticities (2015)
  8. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed volume computation in parallel (2014)
  9. Hampton, Marshall; Roberts, Gareth E.; Santoprete, Manuele: Relative equilibria in the four-vortex problem with two pairs of equal vorticities (2014)
  10. Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S.: Bifurcation analysis and the Conley index in mechanics (2012)
  11. Hampton, Marshall: Finiteness of kite relative equilibria in the five-vortex and five-body problems (2010)
  12. Hampton, Marshall; Moeckel, Richard: Finiteness of stationary configurations of the four-vortex problem (2009)
  13. O’Neil, K. A.: Relative equilibrium and collapse configurations of four point vortices (2007)
  14. O’Neil, Kevin A.: Relative equilibrium and collapse configurations of heterogeneous vortex triple rings (2007)