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A Classification Theorem for Steady Euler Flows
Tarek M. Elgindi, Yupei Huang, Ayman R. Said +1
Fix a bounded, analytic, and simply connected domain We show that all analytic steady states of the Euler equations with stream function are either ra…
Dynamics of Ideal Fluid Flows
Tarek M. Elgindi
We will discuss various aspects of the incompressible Euler equation. We will discuss, in particular, problems related to the least action principle, the existence of special solut…
On the existence of fibered three-dimensional perfect fluid equilibria without continuous Euclidean symmetry
Theodore D. Drivas, Tarek M. Elgindi, Daniel Ginsberg
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in…
Invertibility of a linearized Boussinesq flow: a symbolic approach
Tarek M. Elgindi, Federico Pasqualotto
We develop a computer-assisted symbolic method to show that a linearized Boussinesq flow in self-similar coordinates gives rise to an invertible operator.
Twisting in Hamiltonian Flows and Perfect Fluids
Theodore D. Drivas, Tarek M. Elgindi, In-Jee Jeong
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting…
Finite-time singularity formation for scalar stretching equations
Roberta Bianchini, Tarek M. Elgindi
We consider equations of the type: \[\partial_t Ï= ÏR(Ï),\] for general linear operators in any spatial dimension. We prove that such equations almost always exhibit finite-…