Methods and Applications of Analysis

Structural Stability and Bifurcation for 2-D Incompressible Flows with Symmetry

Chun-Hsiung Hsia, Jian-Guo Liu, and Cheng Wang

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Abstract

This article studies the structure and its evolution of incompressible flows with the anti-symmetry using a combination of rigorous analysis and numerical simulations, with an application to an example of oceanic flow. In particular, necessary and sufficient conditions for 2D divergence-free vector fields with anti-symmetry are obtained, and a detailed numerical simulation for a simplified model of Marsigli oceanic flow is provided to explore and verify the structure and its transitions of the flow. It is expected that the study will lead to useful insights to the understanding of the flow dynamics from both the mathematical and physical points of view.

Article information

Source
Methods Appl. Anal., Volume 15, Number 4 (2008), 495-512.

Dates
First available in Project Euclid: 2 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.maa/1254492831

Mathematical Reviews number (MathSciNet)
MR2550075

Zentralblatt MATH identifier
1180.35410

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics 65M06: Finite difference methods 76D05: Navier-Stokes equations [See also 35Q30]

Keywords
Divergence-free velocity vector structural stability and bifurcation symmetric stability saddle connection

Citation

Hsia, Chun-Hsiung; Liu, Jian-Guo; Wang , Cheng. Structural Stability and Bifurcation for 2-D Incompressible Flows with Symmetry. Methods Appl. Anal. 15 (2008), no. 4, 495--512. https://projecteuclid.org/euclid.maa/1254492831


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