WebOct 6, 2024 · We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform “rigid body” rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter linearly, … WebJul 25, 2024 · Introduction. For axisymmetric incompressible flows without swirl, the (originally three-dimensional) Navier–Stokes and Euler equations can be reduced to two-dimensional mathematical models which are obtained by assuming a cylindrical symmetry for both the physical space variables and the velocity components.
Global stability of two-dimensional and axisymmetric …
WebMay 1, 2007 · This improves on the corresponding results due to Raymond [X. Saint Raymond, Remarks on axisymmetric solutions of the incompressible Euler system, Comm. Partial Differential Equations, 19 (1994) 321–334] and to Chae and Kim [D. Chae, N. Kim, Axisymmetric weak solutions of the 3 D Euler equations for incompressible fluid flows, … WebThis paper focuses on the structure of solutions in a supersonic bubble arising from the three-dimensional transonic flows. Given a velocity distribution on a streamline, we construct a small smooth supersonic-sonic patch for the three-dimensional axisymmetric steady isentropic irrotational Euler equations. This patch can be regarded as the region … chris sheldon amphenol
On the steady axisymmetric vortex rings for 3-D incompressible Euler flows
WebSep 1, 2024 · Global Axisymmetric Euler Flows with Rotation. We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by … WebON THE STEADY AXISYMMETRIC VORTEX RINGS FOR 3-D INCOMPRESSIBLE EULER FLOWS 3 case. Global existence of vortex rings without swirl (i.e., vθ ≡ 0) was first established by Fraenkel and Berger [34]. After this pioneering work, much work is devoted to further studying the existence of vortex rings without swirl. See, e.g., [5, 9, 17, 23, 29, 34 ... WebModels of vorticity growth in Euler Flows I. Axisymmetric flow without swirl Stephen Childress July 25, 2007 Abstract The question of vortex growth in Euler flows leads naturally to the emergence of paired vortex structure and the “geometric” stretching of vortex lines. In the present paper, the first of two papers devoted to this chris sheffield age