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Zbl 1042.35060
Zhou, Yong
Wave breaking for a periodic shallow water equation. (English)
[J] J. Math. Anal. Appl. 290, No. 2, 591-604 (2004). ISSN 0022-247X

Summary: The focus of this paper is on the blow-up of a recently derived one-dimensional shallow water equation which is formally integrable and can be obtained by approximating directly the Hamiltonian for Euler's equations in the shallow water regime. Some new criteria guaranteeing the development of singularities in finite time for strong solutions with regular initial data are obtained for the periodic case.
MSC 2000:
*35Q35 Other equations arising in fluid mechanics
37K10 Completely integrable systems etc.
76B15 Wave motions (fluid mechanics)

Keywords: shallow water equation; periodic solutions; wave breaking; development of singularities

Cited in: Zbl 1126.35056

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