Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article  consider ak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group.  examine both the viscous and inviscid cases. For the case of viscous flows,  prove that Leray--Hopf ak solutions of the three-dimensional Navier--Stokes equations preserve initially imposed symmetry and that such symmetric flows are stable under general three-dimensional perturbations, globally in time.  work in three different contexts: two-and-a-half-dimensional, helical, and axisymmetric flows. In the inviscid case,  observe that as a consequence of recent work by De Lellis and Szekelyhidi, there are genuinely three-dimensional ak solutions of the Euler equations with two-dimensional initial data.  also present two partial results where restrictions on the set of initial data and on the set of admissible solutions rule out spontaneous symmetry breaking; one is due to P.-L. Lions and the other is a consequence of our viscous ...
['C. Bardos', 'M. C. Lopes Filho', 'Dongjuan Niu', 'H. J. Nussenzveig Lopes', 'Edriss S. Titi']
I am writing a research paper on a idea STABILITY OF TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS UNDER THREE-DIMENSIONAL PERTURBATIONS AND INVISCID SYMMETRY BREAKING
[{"from": "human", "value": "I am writing a research paper on a idea STABILITY OF TWO-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS UNDER THREE-DIMENSIONAL PERTURBATIONS AND INVISCID SYMMETRY BREAKING"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this article  consider ak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group.  examine both the viscous and inviscid cases. For the case of viscous flows,  prove that Leray--Hopf ak solutions of the three-dimensional Navier--Stokes equations preserve initially imposed symmetry and that such symmetric flows are stable under general three-dimensional perturbations, globally in time.  work in three different contexts: two-and-a-half-dimensional, helical, and axisymmetric flows. In the inviscid case,  observe that as a consequence of recent work by De Lellis and Szekelyhidi, there are genuinely three-dimensional ak solutions of the Euler equations with two-dimensional initial data.  also present two partial results where restrictions on the set of initial data and on the set of admissible solutions rule out spontaneous symmetry breaking; one is due to P.-L. Lions and the other is a consequence of our viscous ..."}]