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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.