Liouville chains: new hybrid vortex equilibria of the two-dimensional Euler equation
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Adrian Constantin | Miles H. Wheeler | Darren G. Crowdy | Vikas S. Krishnamurthy | D. Crowdy | A. Constantin | V. Krishnamurthy
[1] A. Tur,et al. Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions , 2011, 1201.5271.
[2] M. Pino,et al. Two-dimensional Euler flows with concentrated vorticities , 2010 .
[3] S. G. L. Smith. How do singularities move in potential flow , 2011 .
[4] G. Pedrizzetti,et al. Vortex Dynamics , 2011 .
[5] T. Sakajo. Exact solution to a Liouville equation with Stuart vortex distribution on the surface of a torus , 2019, Proceedings of the Royal Society A.
[6] Miles H. Wheeler,et al. Steady point vortex pair in a field of Stuart-type vorticity , 2019, Journal of Fluid Mechanics.
[7] N. Kudryashov,et al. Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation , 2011, 1112.4350.
[8] P. Clarkson. Vortices and Polynomials , 2008, 0901.0139.
[9] A. Ionescu,et al. Axi‐symmetrization near Point Vortex Solutions for the 2D Euler Equation , 2019, Communications on Pure and Applied Mathematics.
[10] Stuart vortices on a hyperbolic sphere , 2020 .
[11] S. Maslowe,et al. A row of counter-rotating vortices , 1993 .
[12] P. Saffman,et al. Dynamics of vorticity , 1981, Journal of Fluid Mechanics.
[13] Jürgen Moser,et al. On a class of polynomials connected with the Korteweg-deVries equation , 1978 .
[14] Darren Crowdy,et al. Analytical solutions for rotating vortex arrays involving multiple vortex patches , 2005, Journal of Fluid Mechanics.
[15] D. Crowdy,et al. The effect of core size on the speed of compressible hollow vortex streets , 2017, Journal of Fluid Mechanics.
[16] J. L. Burchnall,et al. A Set of Differential Equations which can be Solved by Polynomials , 1930 .
[17] P. Newton. The N-Vortex Problem: Analytical Techniques , 2001 .
[18] D. Crowdy. Point vortex motion on the surface of a sphere with impenetrable boundaries , 2006 .
[19] S. Richardson. Vortices, Liouville's equation and the Bergman kernel function , 1980 .
[20] Juncheng Wei,et al. Convergence for a Liouville equation , 2001 .
[21] D. Crowdy. General solutions to the 2D Liouville equation , 1997 .
[22] K. O'Neil. Minimal polynomial systems for point vortex equilibria , 2006 .
[23] G. K. Morikawa,et al. Interacting Motion of Rectilinear Geostrophic Vortices , 1969 .
[24] H. Helmholtz. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. , 1858 .
[25] Darryl D. Holm,et al. Nonlinear stability of the Kelvin-Stuart cat's eyes flow , 1986 .
[26] L. Fraenkel. On Kelvin–Stuart vortices in a viscous fluid , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[27] T. Bartsch,et al. Erratum to: N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations , 2010 .
[28] D. Crowdy,et al. Speed of a von Kármán point vortex street in a weakly compressible fluid , 2017 .
[29] Christopher C. Green,et al. Analytical solutions for von Kármán streets of hollow vortices , 2011 .
[30] P. Newton,et al. Particle dynamics in a viscously decaying cat’s eye: The effect of finite Schmidt numbers , 1991 .
[31] Miles H. Wheeler,et al. Stuart-type polar vortices on a rotating sphere , 2021, Discrete & Continuous Dynamical Systems - A.
[32] J. T. Stuart. On finite amplitude oscillations in laminar mixing layers , 1967, Journal of Fluid Mechanics.
[33] A. Constantin,et al. Stuart-type vortices on a rotating sphere , 2019, Journal of Fluid Mechanics.
[34] K. O'Neil,et al. Generalized Adler-Moser and Loutsenko polynomials for point vortex equilibria , 2014 .
[35] Igor Loutsenko. Equilibrium of charges and differential equations solved by polynomials , 2003, math-ph/0304008.
[36] S. Friedlander. Lectures on Stability and Instability of an Ideal Fluid , 1999 .
[37] Some classes of two-dimensional vortex flows of an ideal fluid , 1989 .
[38] D. Crowdy. Exact solutions for rotating vortex arrays with finite-area cores , 2002, Journal of Fluid Mechanics.
[39] Sheila E. Widnall,et al. The structure of organized vortices in a free shear layer , 1979, Journal of Fluid Mechanics.
[40] T. Bartsch,et al. N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations , 2010 .
[41] D. Crowdy. A class of exact multipolar vortices , 1999 .
[42] D. Crowdy. Polygonal N-vortex arrays: A Stuart model , 2003 .
[43] H. McKean,et al. Rational and elliptic solutions of the korteweg‐de vries equation and a related many‐body problem , 1977 .
[44] K. O'Neil. Relative equilibria of point vortices and linear vortex sheets , 2018, Physics of Fluids.
[45] K. O'Neil. Dipole and Multipole Flows with Point Vortices and Vortex Sheets , 2018, Regular and Chaotic Dynamics.
[46] Hassan Aref,et al. Point vortex dynamics: A classical mathematics playground , 2007 .
[47] P. Newton,et al. Particle dynamics and mixing in a viscously decaying shear layer , 1991, Journal of Fluid Mechanics.
[48] Miles H. Wheeler,et al. A transformation between stationary point vortex equilibria , 2020, Proceedings of the Royal Society A.
[49] A. Tur,et al. Point vortices with a rational necklace: New exact stationary solutions of the two-dimensional Euler equation , 2004 .
[50] D. Crowdy. Stuart vortices on a sphere , 2003, Journal of Fluid Mechanics.
[51] K. O'Neil. Stationary configurations of point vortices , 1987 .
[52] F. Grünbaum,et al. Differential equations in the spectral parameter , 1986 .
[53] H. Aref. Relative equilibria of point vortices and the fundamental theorem of algebra , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[54] D. W. Moore,et al. On steady compressible flows with compact vorticity; the compressible Stuart vortex , 2000, Journal of Fluid Mechanics.
[55] P. G. Drazin,et al. Philip Drazin and Norman Riley: The Navier–Stokes equations : a classification of flows and exact solutions , 2011, Theoretical and Computational Fluid Dynamics.