1985•Communications on Pure and Applied MathematicsRequires access

A simple one‐dimensional model for the three‐dimensional vorticity equation

Peter Constantin, Peter D. Lax, Andrew J. Majda

Abstract

Abstract A simple qualitative one‐dimensional model for the 3‐D vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the 3‐D Euler equations.

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Available abstract

Key concepts: Vorticity, Euler equations, Vorticity equation, Simple (philosophy), Mathematics, Simplicity, Computation, Vortex