Well-posedness and blow-up solution for the stochastic Dullin-Gottwald-Holm equation

2019 ◽  
Vol 60 (8) ◽  
pp. 083513 ◽  
Author(s):  
Wujun Lv ◽  
Ping He ◽  
Qinghua Wang
Keyword(s):  
Blow Up ◽  
Well Posedness ◽  
Holm Equation

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

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, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Well Posedness ◽  
Asymptotic Profile ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consider the asymptotic behavior of solutions.

scholarly journals Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yonghui Zhou ◽  
Shuguan Ji
Keyword(s):  
Wave Breaking ◽  
Blow Up ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Necessary And Sufficient Condition ◽  
Unique Global Solution ◽  
Holm Equation ◽  
The Moment ◽  
Sign Conditions ◽  
Necessary And Sufficient

<p style='text-indent:20px;'>In this paper, we mainly study several problems on the weakly dissipative generalized Camassa-Holm equation. We first establish the local well-posedness of solutions by Kato's semigroup theory. We then derive the necessary and sufficient condition of the blow-up of solutions and a criteria to guarantee occurrence of wave breaking. Moreover, when the solution blows up, we obtain the precise blow-up rate. We finally show that the equation has a unique global solution provided the moment density associated with their initial datum satisfies appropriate sign conditions.</p>

scholarly journals Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

2007 ◽  
Vol 19 (3) ◽  
pp. 493-513 ◽  
Author(s):  
Joachim Escher ◽  
◽  
Olaf Lechtenfeld ◽  
Zhaoyang Yin ◽  
◽  
...  
Keyword(s):  
Blow Up ◽  
Well Posedness ◽  
Holm Equation
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