Stokes waves are unstable, even very small ones
EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 71-78

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WS: it is difficult to write about Thomas Kappeler in the past tense. He was a brilliant mathematician, but more importantly he was a wonderfully open, generous, and friendly person. I was fortunate that we had many opportunities to spend time together and discuss mathematics. I greatly miss him. A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. Even Stokes waves of very small amplitude are unstable when subjected to various perturbations. We present a brief survey of this phenomenon with emphasis on transverse perturbations.
DOI : 10.4171/emss/90
Classification : 76B07, 35Q35, 35R35, 35C07, 35B35
Mots-clés : Stokes waves, gravity waves, transverse instabilities, unstable eigenvalues, infinite depth

Ryan P. Creedon  1   ; Huy Q. Nguyen  2   ; Walter A. Strauss  3

1 University of Washington, Seattle, USA; Brown University, Providence, USA
2 University of Maryland, College Park, USA
3 Brown University, Providence, USA
Ryan P. Creedon; Huy Q. Nguyen; Walter A. Strauss. Stokes waves are unstable, even very small ones. EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 71-78. doi: 10.4171/emss/90
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