The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the se...The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.展开更多
In this paper, we study the Cauchy problem of the Camassa-Holm equation with a zero order dissipation. We establish local well-posedness and investigate the blow-up phenomena for the equation.
The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on th...The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs （R） with 1 〈 s ≤ 3/2 is derived.展开更多
This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann ...This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.展开更多
基金Supported by the National Natural Science Foundation of China(No.11061003,11301097)Guangxi Natural Science Foundation Grant(No.2013GXNSFAA019001)Guangxi Science Research Item(No.2013YB170)
文摘The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.
文摘In this paper, we study the Cauchy problem of the Camassa-Holm equation with a zero order dissipation. We establish local well-posedness and investigate the blow-up phenomena for the equation.
基金Supported by Key Project of Chinese Ministry of Education (Grant No.109140)the SWUFE's third period construction item funds of the 211 project (Grant No.211D3T06)
文摘The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs （R） with 1 〈 s ≤ 3/2 is derived.
基金supported by the National Natural Science Foundation of China(Nos.11901302,11401180)the Natural Science Foundation from Jiangsu province BK20171029the Academic Discipline Project of Shanghai Dianji University(No.16JCXK02)。
文摘This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.
