The Kuramoto-Sivashinsky Equation

Cheyne Weis; John C. Baez; Steve Huntsman

The Kuramoto-Sivashinsky Equation

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arxiv 2210.01711 v1 pith:F6IP2CYS submitted 2022-10-04 math.AP math.DSnlin.CD

John C. Baez , Steve Huntsman , Cheyne Weis This is my paper

classification math.APmath.DSnlin.CD

keywords equationkuramoto-sivashinskymodelprecisesimplestripestimeappears

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The Kuramoto-Sivashinsky equation was introduced as a simple 1-dimensional model of instabilities in flames, but it turned out to mathematically fascinating in its own right. One reason is that this equation is a simple model of Galilean-invariant chaos with an arrow of time. Starting from random initial conditions, manifestly time-asymmetric stripe-like patterns emerge. As we move forward in time, it appears that these stripes are born and merge, but do not die or split. We pose a precise conjecture to this effect, which requires a precise definition of 'stripes'.

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