| Abstract: |
| Vortex filaments are fundamental structures in three-dimensional incompressible fluid dynamics, capturing the concentration of vorticity along curves and providing a natural framework for the analysis of coherent structures. Understanding their evolution under the 3D Navier-Stokes equations remains a challenging problem, especially in regimes where geometric features of the flow play a significant role.
In this talk, we consider vortex filaments with helical structure, which arise naturally in flows exhibiting symmetry and offer a tractable setting to investigate the interplay between geometry and diffusion. Our analysis applies to vortex filaments of arbitrary size and without vanishing swirl assumption. After introducing the mathematical formulation of the problem and the main analytical difficulties, we present new results concerning the existence, uniqueness, and evolution of such helical vortex filaments in the Navier-Stokes setting. |
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