A simple justification of the singular limit for equatorial shallow-water dynamics

2009 ◽  
Vol 62 (3) ◽  
pp. 322-333 ◽  
Author(s):  
Alexandre Dutrifoy ◽  
Steven Schochet ◽  
Andrew J. Majda
Keyword(s):  
Shallow Water ◽  
Singular Limit ◽  
Water Dynamics ◽  
Shallow Water Dynamics

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

scholarly journals Shallow water dynamics on linear shear flows and plane beaches

2017 ◽  
Vol 29 (7) ◽  
pp. 073602 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Water Dynamics ◽  
Linear Shear ◽  
Shallow Water Dynamics
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