In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded doma...In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.展开更多
In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means o...In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.展开更多
In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal...In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal to a global attractor Aj in HJ （Ω） （i ≠j, i, j = 1, 2, .. m）.展开更多
In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is sho...In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E1.展开更多
文摘In this paper we prove that the initial-boundary value problem for the nonlinear evolution equation ut = △u ＋ λu - u^3 possesses a global attractor in Sobolev space H^k for all k≥0, which attracts any bounded domain of H^k（Ω） in the H^k-norm. This result is established by using an iteration technique and regularity estimates for linear semigroup of operator, which extends the classical result from the case k ∈ [0, 1] to the case k∈ [0, ∞）.
基金Supported by the NSF of China (Nos. 10571142, 10771167)
文摘In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.
基金Supported by the NationalNatural Science Foundation of China(No.11061003)Guangxi Natural Science Foundation Grant(No.0832065)Guangxi excellent talents funded project(No.0825)
文摘In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor .Ai in Hi（Ω） is actually equal to a global attractor Aj in HJ （Ω） （i ≠j, i, j = 1, 2, .. m）.
基金Supported by the National Natural Science Foundation of China (No.19861004)
文摘In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E1.
