Huang, Zhehao; Liu, Zhengrong Uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations. (English) Zbl 1338.37114 Abstr. Appl. Anal. 2013, Article ID 492847, 17 p. (2013). Summary: We consider the uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations in the periodic box \([0,l]^3\) in this paper. We associate with the concepts of uniform attractor and random attractor and produce the concept of uniformly random attractor for a process. Then we establish the existence of the uniformly random attractor in \(D(A^{1/2})\) and \(D(A)\) for the equations. MSC: 37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35Q35 PDEs in connection with fluid mechanics 37L55 Infinite-dimensional random dynamical systems; stochastic equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Camassa, R.; Holm, D. D., An integrable shallow water equation with peaked solitons, Physical Review Letters, 71, 11, 1661-1664 (1993) · Zbl 0972.35521 · doi:10.1103/PhysRevLett.71.1661 [2] Camassa, R.; Holm, D. D.; Hyman, J. M., An new integrable shallow water equation, Advances in Applied Mechanics, 31, 1-33 (1994) · Zbl 0808.76011 · doi:10.1016/S0065-2156(08)70254-0 [3] Dullin, H. R.; Gottwald, G. A.; Holm, D. 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