Uniqueness of axisymmetric viscous flows originating from positive linear combinations of circular vortex filaments

TL;DR

This paper proves the uniqueness of axisymmetric Navier-Stokes solutions without swirl for initial data composed of positive linear combinations of Dirac masses, extending previous work on vortex filament flows.

Contribution

It establishes the uniqueness of solutions for a specific class of initial data in axisymmetric viscous flows, advancing understanding of vortex filament dynamics.

Findings

Uniqueness of solutions for initial data as positive linear combinations of Dirac masses.

Extension of prior results to axisymmetric Navier-Stokes equations without swirl.

Provides mathematical foundation for vortex filament flow analysis.

Abstract

Following the recent papers [9] and [10] by T. Gallay and V. \u{S}ver\'ak, in the line of work initiated by H. Feng and V. \u{S}ver\'ak in their paper [3], we prove the uniqueness of a solution of the axisymmetric Navier-Stokes equations without swirl when the initial data is a positive linear combination of Dirac masses.