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arxiv: 2301.11090 · v2 · pith:NTGJOP2Nnew · submitted 2023-01-26 · 🧮 math.AP

Self-similar axisymmetric flows with swirl

Theodoros Katsaounis , Ioanna Mousikou , Athanasios E. Tzavaras This is my paper
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keywords solutionsaxisymmetricconsiderself-similarstationaryviscosityboundaryclass
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We consider an infinite vortex line in a fluid which interacts with a boundary surface as a simplified model for tornadoes. We study self-similar solutions for stationary axisymmetric Navier-Stokes equations and investigate the types of motion which are compatible with this structure when viscosity is non-negative. For viscosity equal to zero, we construct a class of explicit stationary solutions. We then consider solutions with slip discontinuity and show that they do not exist in this framework.

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  1. Global Regularity for Axisymmetric Navier--Stokes Flows with Swirl

    math.AP 2026-06 unverdicted novelty 7.0

    Proves global regularity for axisymmetric 3D Navier-Stokes flows with swirl by controlling near-axis source terms via circulation identities and Hardy estimates.