Unraveling the Mysteries of Fluid Flow

Paper Title:

A rigidity result for the Euler equations in an annulus

Published on:

11 June 2023

Primary Category:

Analysis of PDEs

Paper Authors:

Yuchen Wang,

Weicheng Zhan

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Key Details

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Proves circular flow theorem for steady Euler flows in a 2D annulus with no stagnation points

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Stream function satisfies a nonlinear elliptic PDE due to streamline geometry

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Solutions of the PDE exhibit local radial symmetry properties

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Symmetry of stream function implies the flow has circular streamlines

Explore the topics in this paper

annuli

differential equations

fluid dynamics

nonlinear systems

streamlines

AI generated summary

Unraveling the Mysteries of Fluid Flow

This paper proves that steady fluid flows with no stagnation points in a 2D annulus must follow circular streamlines. The proof relies on analyzing the geometry of streamlines and symmetry properties of related differential equations. This addresses an open question about the extent to which fluid flows inherit the symmetry of their domain.