Pith. sign in

REVIEW 1 cited by

Nonlinear stability of plane ideal flows in a periodic channel

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.23857 v2 pith:HZDXWM7R submitted 2025-03-31 math.AP

Guodong Wang This is my paper
classification math.AP
keywords channelarnoldequationeulerflowsperiodicstabilityanalysis
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In this paper, we establish two stability theorems for steady or traveling solutions of the two-dimensional incompressible Euler equation in a finite periodic channel, extending Arnold's classical work from the 1960s. Compared to Arnold's approach, we employ a compactness argument rather than relying on the negative definiteness of the energy-Casimir functional. The isovortical property of the Euler equation and Burton's rearrangement theory play an essential role in our analysis. As a corollary, we prove for the first time the existence of a class of stable non-shear flows when the ratio of the channel's height to its length is less than or equal to $\sqrt{3}/2.$ Two rigidity results are also obtained as byproducts.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Orbital Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus

    math.AP 2025-08 accept novelty 6.0 of 10

    First Laplacian eigenstates on flat 2-tori of any shape are orbitally stable for 2D Euler dynamics up to translations, including new stable sinusoidal flows on hexagonal tori.

Pith tools