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Theory and simulation of real and ideal magnetohydrodynamic turbulence
The constrained planar Nvortex problem: I. Integrability
1.  Department of Aerospace & Mechanical Engineering and Department of Mathematics, University of Southern California, Los Angeles, CA 900891191, United States, United States, United States 
[1] 
Björn Gebhard. Periodic solutions for the Nvortex problem via a superposition principle. Discrete & Continuous Dynamical Systems  A, 2018, 38 (11) : 54435460. doi: 10.3934/dcds.2018240 
[2] 
P.K. Newton. Nvortex equilibrium theory. Discrete & Continuous Dynamical Systems  A, 2007, 19 (2) : 411418. doi: 10.3934/dcds.2007.19.411 
[3] 
Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of some particle systems with twobody interactions and of the dislocation dynamics. Discrete & Continuous Dynamical Systems  A, 2009, 23 (3) : 785826. doi: 10.3934/dcds.2009.23.785 
[4] 
Božidar Jovanović, Vladimir Jovanović. Virtual billiards in pseudo–euclidean spaces: Discrete hamiltonian and contact integrability. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 51635190. doi: 10.3934/dcds.2017224 
[5] 
Shaoyun Shi, Wenlei Li. Nonintegrability of generalized YangMills Hamiltonian system. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 16451655. doi: 10.3934/dcds.2013.33.1645 
[6] 
Joseph Nebus. The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments. Discrete & Continuous Dynamical Systems  B, 2005, 5 (1) : 125136. doi: 10.3934/dcdsb.2005.5.125 
[7] 
Juan J. MoralesRuiz, Sergi Simon. On the meromorphic nonintegrability of some $N$body problems. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12251273. doi: 10.3934/dcds.2009.24.1225 
[8] 
Younghun Hong. Strichartz estimates for $N$body Schrödinger operators with small potential interactions. Discrete & Continuous Dynamical Systems  A, 2017, 37 (10) : 53555365. doi: 10.3934/dcds.2017233 
[9] 
Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. RiemannHilbert problem, integrability and reductions. Journal of Geometric Mechanics, 2019, 11 (2) : 167185. doi: 10.3934/jgm.2019009 
[10] 
Xavier Perrot, Xavier Carton. Pointvortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete & Continuous Dynamical Systems  B, 2009, 11 (4) : 971995. doi: 10.3934/dcdsb.2009.11.971 
[11] 
Guillaume Duval, Andrzej J. Maciejewski. Integrability of Hamiltonian systems with homogeneous potentials of degrees $\pm 2$. An application of higher order variational equations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 45894615. doi: 10.3934/dcds.2014.34.4589 
[12] 
Mitsuru Shibayama. Nonintegrability criterion for homogeneous Hamiltonian systems via blowingup technique of singularities. Discrete & Continuous Dynamical Systems  A, 2015, 35 (8) : 37073719. doi: 10.3934/dcds.2015.35.3707 
[13] 
A. Ghose Choudhury, Partha Guha. Chiellini integrability condition, planar isochronous systems and Hamiltonian structures of Liénard equation. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 24652478. doi: 10.3934/dcdsb.2017126 
[14] 
Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 299312. doi: 10.3934/dcds.2011.30.299 
[15] 
Zhong Tan, Jianfeng Zhou. Higher integrability of weak solution of a nonlinear problem arising in the electrorheological fluids. Communications on Pure & Applied Analysis, 2016, 15 (4) : 13351350. doi: 10.3934/cpaa.2016.15.1335 
[16] 
Petteri Piiroinen, Martin Simon. Probabilistic interpretation of the Calderón problem. Inverse Problems & Imaging, 2017, 11 (3) : 553575. doi: 10.3934/ipi.2017026 
[17] 
Yong Zhou, Jishan Fan. Regularity criteria of strong solutions to a problem of magnetoelastic interactions. Communications on Pure & Applied Analysis, 2010, 9 (6) : 16971704. doi: 10.3934/cpaa.2010.9.1697 
[18] 
Shaoyong Lai, Qichang Xie. A selection problem for a constrained linear regression model. Journal of Industrial & Management Optimization, 2008, 4 (4) : 757766. doi: 10.3934/jimo.2008.4.757 
[19] 
Ludovick Gagnon. Qualitative description of the particle trajectories for the Nsolitons solution of the Kortewegde Vries equation. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 14891507. doi: 10.3934/dcds.2017061 
[20] 
D. Novikov and S. Yakovenko. Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems. Electronic Research Announcements, 1999, 5: 5565. 
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