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Search Results: 1 - 10 of 12024 matches for " Zhaoyang Yin "
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On the Cauchy problem for a nonlinearly dispersive wave equation
Zhaoyang Yin
Mathematics , 2003, DOI: 10.2991/jnmp.2003.10.1.2
Abstract: We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite times. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data.
Well-posedness, global existence and blow-up phenomena for an integrable multi-component Camassa-Holm system
Zeng Zhang,Zhaoyang Yin
Physics , 2014,
Abstract: This paper is concerned with a multi-component Camassa-Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa-Holm type systems as special cases. In this paper, we first establish the local well-posedness and a continuation criterion for the system, then we present several global existence or blow-up results for two important integrable two-component subsystems. Our obtained results cover and improve recent results in \cite{Gui,yan}.
Blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system
Jingjing Liu,Zhaoyang Yin
Mathematics , 2010,
Abstract: This paper is concerned with blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system. We first derive the precise blow-up scenario for strong solutions to the system. Then, we present several new blow-up results of strong solutions and a new global existence result to the system. Our obtained results for the system are sharp and improve considerably earlier results.
Global weak solutions for a periodic two-component $μ$-Hunter-Saxton system
Jingjing Liu,Zhaoyang Yin
Mathematics , 2010,
Abstract: This paper is concerned with global existence of weak solution for a periodic two-component $\mu$-Hunter-Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component $\mu$-Hunter-Saxton system.
On the Cauchy problem of a two-component b-family equation
Jingjing Liu,Zhaoyang Yin
Mathematics , 2010,
Abstract: In this paper, we study the Cauchy problem of a two-component b-family equation. We first establish the local well-posedness for a two-component b-family equation by Kato's semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the equation. Moreover, we present several blow-up results for strong solutions to the equation.
On the Cauchy problem of a periodic 2-component $μ$-Hunter-Saxton equation
Jingjing Liu,Zhaoyang Yin
Mathematics , 2010,
Abstract: In this paper, we study the Cauchy problem of a periodic 2-component $\mu$-Hunter-Saxton system. We first establish the local well-posedness for the periodic 2-component $\mu$-Hunter-Saxton system by Kato's semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the system. Moreover, we present a blow-up result for strong solutions to the system. Finally, we give a global existence result to the system.
Global existence and blow-up phenomena for a periodic 2-component Camassa-Holm equation with vorticity
Qiaoyi Hu,Zhaoyang Yin
Mathematics , 2011,
Abstract: We first establish local well-posedness for a periodic 2-component Camassa-Holm equation with vorticity. We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation.
On the Cauchy problem of a weakly dissipative $μ$HS equation
Jingjing Liu,Zhaoyang Yin
Mathematics , 2011,
Abstract: In this paper, we study the Cauchy problem of a weakly dissipative $\mu$HS equation. We first establish the local well-posedness for the weakly dissipative $\mu$HS equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.
Stability of peakons for a modified Camassa-Holm equation
Xingxing Liu,Zhaoyang Yin
Mathematics , 2013,
Abstract: In this paper, we investigate the orbital stability of peakons for a modified Camassa-Holm equation with cubic nonlinearity derived from the two-dimensional Euler equation. By overcoming the difficulties caused by one of the complicated conservation laws and introducing a new auxiliary function, we prove the orbital stability of peakons for the equation.
Global Well-posedness for the Generalized Navier-Stokes System
Zeng Zhang,Zhaoyang Yin
Mathematics , 2013,
Abstract: In this paper we investigate well-posedness of the Cauchy problem of the three dimensional generalized Navier-Stokes system. We first establish local well-posedness of the GNS system for any initial data in the Fourier-Herz space $\chi^{-1}$. Then we show that if the $\chi^{-1}$ norm of the initial data is smaller than C$\nu$ in the GNS system where $\nu$ is the viscosity coefficient, the corresponding solution exists globally in time. Moreover, we prove global well-posedness of the Navier-Stokes system without norm restrictions on the corresponding solutions provided the $\chi^{-1}$ norm of the initial data is less than $\nu.$ Our obtained results cover and improve recent results in \cite{Zhen Lei,wu}.
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