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Lectures on the Onsager conjecture
New statistical symmetries of the multipoint equations and its importance for turbulent scaling laws
1.  Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Petersenstr. 30, 64287 Darmstadt, Germany, Germany 
[1] 
John R. Graef, Shapour Heidarkhani, Lingju Kong. Existence of nontrivial solutions to systems of multipoint boundary value problems. Conference Publications, 2013, 2013 (special) : 273281. doi: 10.3934/proc.2013.2013.273 
[2] 
Lingju Kong, Qingkai Kong. Existence of nodal solutions of multipoint boundary value problems. Conference Publications, 2009, 2009 (Special) : 457465. doi: 10.3934/proc.2009.2009.457 
[3] 
Yu Tian, John R. Graef, Lingju Kong, Min Wang. Existence of solutions to a multipoint boundary value problem for a second order differential system via the dual least action principle. Conference Publications, 2013, 2013 (special) : 759769. doi: 10.3934/proc.2013.2013.759 
[4] 
Franz W. Kamber and Peter W. Michor. Completing Lie algebra actions to Lie group actions. Electronic Research Announcements, 2004, 10: 110. 
[5] 
Katarzyna Grabowska, Marcin Zając. The Tulczyjew triple in mechanics on a Lie group. Journal of Geometric Mechanics, 2016, 8 (4) : 413435. doi: 10.3934/jgm.2016014 
[6] 
Elena Celledoni, Brynjulf Owren. Preserving first integrals with symmetric Lie group methods. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 977990. doi: 10.3934/dcds.2014.34.977 
[7] 
Emma Hoarau, Claire david@lmm.jussieu.fr David, Pierre Sagaut, ThiênHiêp Lê. Lie group study of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 495505. doi: 10.3934/proc.2007.2007.495 
[8] 
Andreas Widder, Christian Kuehn. Heterogeneous population dynamics and scaling laws near epidemic outbreaks. Mathematical Biosciences & Engineering, 2016, 13 (5) : 10931118. doi: 10.3934/mbe.2016032 
[9] 
Dmitry V. Zenkov. Linear conservation laws of nonholonomic systems with symmetry. Conference Publications, 2003, 2003 (Special) : 967976. doi: 10.3934/proc.2003.2003.967 
[10] 
L. Bakker. A reducible representation of the generalized symmetry group of a quasiperiodic flow. Conference Publications, 2003, 2003 (Special) : 6877. doi: 10.3934/proc.2003.2003.68 
[11] 
Eduardo Martínez. Classical field theory on Lie algebroids: Multisymplectic formalism. Journal of Geometric Mechanics, 2018, 10 (1) : 93138. doi: 10.3934/jgm.2018004 
[12] 
Giovanni De Matteis, Gianni Manno. Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations. Communications on Pure & Applied Analysis, 2014, 13 (1) : 453481. doi: 10.3934/cpaa.2014.13.453 
[13] 
María Rosa, María de los Santos Bruzón, María de la Luz Gandarias. Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term. Discrete & Continuous Dynamical Systems  S, 2015, 8 (6) : 13311339. doi: 10.3934/dcdss.2015.8.1331 
[14] 
Gerald Sommer, Di Zang. Parity symmetry in multidimensional signals. Communications on Pure & Applied Analysis, 2007, 6 (3) : 829852. doi: 10.3934/cpaa.2007.6.829 
[15] 
Yong Hong Wu, B. Wiwatanapataphee. Modelling of turbulent flow and multiphase heat transfer under electromagnetic force. Discrete & Continuous Dynamical Systems  B, 2007, 8 (3) : 695706. doi: 10.3934/dcdsb.2007.8.695 
[16] 
Gunduz Caginalp, Mark DeSantis. Multigroup asset flow equations and stability. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 109150. doi: 10.3934/dcdsb.2011.16.109 
[17] 
Olof Heden, Fabio Pasticci, Thomas Westerbäck. On the existence of extended perfect binary codes with trivial symmetry group. Advances in Mathematics of Communications, 2009, 3 (3) : 295309. doi: 10.3934/amc.2009.3.295 
[18] 
David BlázquezSanz, Juan J. MoralesRuiz. Lie's reduction method and differential Galois theory in the complex analytic context. Discrete & Continuous Dynamical Systems  A, 2012, 32 (2) : 353379. doi: 10.3934/dcds.2012.32.353 
[19] 
Melvin Leok, Diana Sosa. Dirac structures and HamiltonJacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421442. doi: 10.3934/jgm.2012.4.421 
[20] 
Jingxian Sun, Shouchuan Hu. Flowinvariant sets and critical point theory. Discrete & Continuous Dynamical Systems  A, 2003, 9 (2) : 483496. doi: 10.3934/dcds.2003.9.483 
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