scholarly journals Wave breaking and global existence for the periodic rotation-Camassa-Holm system

2017 ◽  
Vol 37 (4) ◽  
pp. 2243-2257 ◽  
Author(s):  
Ying Zhang ◽  
Keyword(s):  
Global Existence ◽  
Wave Breaking ◽  
Periodic Rotation

Wave breaking analysis for the periodic rotation-two-component Camassa–Holm system

2019 ◽  
Vol 187 ◽  
pp. 214-228
Author(s):  
Jingjing Liu ◽  
Patrizia Pucci ◽  
Qihu Zhang
Keyword(s):  
Wave Breaking ◽  
Periodic Rotation ◽  
Two Component

scholarly journals The dynamic properties of solutions for a nonlinear shallow water equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yeqin Su ◽  
Shaoyong Lai ◽  
Sen Ming
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Shallow Water ◽  
Wave Breaking ◽  
Dynamic Properties ◽  
Shallow Water Equation ◽  
Propagation Speed ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Infinite Propagation Speed

Abstract The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation are derived under certain assumptions. In addition, the effects of coefficients λ, β, a, b, and index k in the equation are illustrated.

scholarly journals Publisher Correction to: On the stochastic Dullin–Gottwald–Holm equation: global existence and wave-breaking phenomena

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Christian Rohde ◽  
Hao Tang
Keyword(s):  
Global Existence ◽  
Wave Breaking ◽  
Original Publication ◽  
Holm Equation

During the typesetting process, some misprints have been introduced in the original publication of the article.

scholarly journals On the stochastic Dullin–Gottwald–Holm equation: global existence and wave-breaking phenomena

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Christian Rohde ◽  
Hao Tang
Keyword(s):  
Global Existence ◽  
Wave Breaking ◽  
Evolution Equations ◽  
Blow Up ◽  
Local Existence ◽  
Strong Solutions ◽  
Local Existence And Uniqueness ◽  
Holm Equation ◽  
Nonlinear Noise ◽  
Pathwise Solutions

AbstractWe consider a class of stochastic evolution equations that include in particular the stochastic Camassa–Holm equation. For the initial value problem on a torus, we first establish the local existence and uniqueness of pathwise solutions in the Sobolev spaces $$H^s$$ H s with $$s>3/2$$ s > 3 / 2 . Then we show that strong enough nonlinear noise can prevent blow-up almost surely. To analyze the effects of weaker noise, we consider a linearly multiplicative noise with non-autonomous pre-factor. Then, we formulate precise conditions on the initial data that lead to global existence of strong solutions or to blow-up. The blow-up occurs as wave breaking. For blow-up with positive probability, we derive lower bounds for these probabilities. Finally, the blow-up rate of these solutions is precisely analyzed.

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