Existence of stationary turbulent flows with variable positive vortex intensity

TL;DR

This paper proves the existence of stationary turbulent flows with positive vortex circulation on complex domains, covering most inverse temperature values and extending previous mathematical analysis in fluid dynamics.

Contribution

It establishes the existence of such flows for all but a quantized set of inverse temperature values, advancing understanding of vortex behavior in turbulent flows.

Findings

Solutions exist for all real inverse temperature values except a quantized set.

Construction applies to non simply connected domains.

Potential blow-up phenomena are identified for certain parameter values.

Abstract

We prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in [J. Diff. Equ. 260 (2016), 339-369].