scholarly journals Well-posedness and blow-up phenomena for a higher order shallow water equation

2011 ◽  
Vol 251 (12) ◽  
pp. 3488-3499 ◽  
Author(s):  
Chunlai Mu ◽  
Shouming Zhou ◽  
Rong Zeng
Keyword(s):  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Higher Order ◽  
Well Posedness

scholarly journals Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation

2014 ◽  
Vol 12 ◽  
pp. 10-20
Author(s):  
Jiang Bo Zhou ◽  
Jun De Chen ◽  
Wen Bing Zhang
Keyword(s):  
Global Existence ◽  
Shallow Water ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Holm Equation ◽  
Special Cases ◽  
Long Time

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

scholarly journals Well-posedness and derivative blow-up for a dispersionless regularized shallow water system

Nonlinearity ◽  
2019 ◽  
Vol 32 (11) ◽  
pp. 4346-4376
Author(s):  
Jian-Guo Liu ◽  
Robert L Pego ◽  
Yue Pu
Keyword(s):  
Shallow Water ◽  
Blow Up ◽  
Water System ◽  
Well Posedness ◽  
Shallow Water System

Wave breaking and shock waves for a periodic shallow water equation

2007 ◽  
Vol 365 (1858) ◽  
pp. 2281-2289 ◽  
Author(s):  
Joachim Escher
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Wave Breaking ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Strong Solutions ◽  
Global Weak Solutions ◽  
Initial Profile ◽  
And Shock Waves ◽  
Periodic Shock

This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock waves to the equation under discussion.

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