On the wave‐breaking phenomena for the two‐component Dullin–Gottwald–Holm system | Zendy

Guo Fei | Zendy; Gao Hongjun | Zendy; Liu Yue | Zendy

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On the wave‐breaking phenomena for the two‐component Dullin–Gottwald–Holm system

Author(s) -

Guo Fei,

Gao Hongjun,

Liu Yue

Publication year - 2012

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/jds035

Subject(s) - breaking wave , gravitational singularity , euler equations , component (thermodynamics) , vorticity , mathematics , mathematical analysis , flow (mathematics) , constant (computer programming) , euler's formula , waves and shallow water , physics , vortex , mechanics , geometry , computer science , thermodynamics , wave propagation , quantum mechanics , programming language

Considered herein is the well‐posedness problem of the two‐component Dullin–Gottwald–Holm system, which can be derived from the Euler equation with constant vorticity in shallow water waves moving over a linear shear flow. It is shown that the solutions to this system have singularities that correspond to wave breaking. Moreover, two sufficient conditions to guarantee wave‐breaking phenomena are given. Finally, a result of global solutions is formulated.

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