John C. Baez, Steve Huntsman, Cheyne Weis
Published 2022-10-04Version 1
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'.
Comments: 3 pages, 2 figures
Journal: Notices Amer. Math. Soc. 69 (2022), 1581-1583
Uncertainty estimates and L_2 bounds for the Kuramoto-Sivashinsky equation
On a nonlocal analog of the Kuramoto-Sivashinsky equation
New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations
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