Abstract
Steadily rotating solutions of the Kuramoto-Sivashinsky equationu t +Δ 2 u+Δ+¦▽u¦ 2=c 2 are studied. These solutions bifurcate from the steady radial solution of the above equation. For large values ofc and angular velocities ω such thatN¦ω¦<2c<(N+1)¦ω¦, we show that there exists a 2N-1 family of bifurcating solutions. The proof is based on a certain generic transversality assumption. A computer-assisted proof of this assumption is given for 1⩽N⩽10.
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Michelson, D. Rotating bunsen flames as solutions of the Kuramoto-Sivashinsky equation. J Dyn Diff Equat 5, 375–415 (1993). https://doi.org/10.1007/BF01053530
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DOI: https://doi.org/10.1007/BF01053530
Key words
- Bunsen flames
- Kuramoto-Sivashinsky equation
- rotating solutions
- interval arithmetic
- computer-assisted proofs