What question did this study set out to answer?

This research aims to characterize steady states of the Euler equations and identify conditions for laminar flows in various domains.

A Geometric Characterization of Steady Laminar Flow

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We study steady laminar flow states, revealing properties and symmetries in specific domains, indicating implications for non-shear states.

This research aims to characterize steady states of the Euler equations and identify conditions for laminar flows in various domains.
Analyzed Euler equations on periodic channels and annuli.
Demonstrated isolation of shear flows from non-shear stationary states.
Established conditions for smooth non-shear steady states and quasiperiodic solutions.
Proved that laminar steady Euler flows must be either parallel or circular on compact doubly connected domains.
Showed that in small neighborhoods around Poiseuille flow, all stationary solutions are shear flows.
Established rigidity around Poiseuille showing existence of non-shear steady states and quasiperiodic solutions.

Drivas et al. (2026) studied this question.

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We study steady laminar flow states, revealing properties and symmetries in specific domains, indicating implications for non-shear states.