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math.AP2012
Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
Tudor Ratiu, Olga Rozanova
We prove that the smooth solutions to the Cauchy problem for the compressible general three-dimensional Ericksen--Leslie system modeling nematic liquid crystal flow with conserved…
math-ph2012
Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems
Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu
The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are…