Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier G\'omez-Serrano, Jaemin Park, Jia Shi, Yao Yao
TL;DR
This paper constructs new solutions for the vortex sheet equation that rotate uniformly, using bifurcation analysis from circular configurations with constant vorticity, employing Lyapunov-Schmidt reduction and second order expansions.
Contribution
It introduces novel uniformly-rotating vortex sheet solutions bifurcating from circles, advancing understanding of vortex sheet dynamics.
Findings
New uniformly-rotating vortex sheet solutions constructed.
Bifurcation from circular vortex configurations demonstrated.
Methodology involves Lyapunov-Schmidt reduction and second order expansion.
Abstract
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via a Lyapunov-Schmidt reduction and a second order expansion of the reduced system.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Navier-Stokes equation solutions · Stability and Controllability of Differential Equations