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In this paper, we construct an approximation sequence by a smoothing method for continuous functions; then, we prove that there exists a unique solution to reflected backward stochastic differential equations driven by G-Brownian motion when the coefficients do not satisfy the Lipschitz condition. Moreover, we prove a comparison theorem. [ABSTRACT FROM AUTHOR]

The 2D magnetohydrodynamics equations with horizontal dissipation and horizontal magnetic diffusion are considered. The classical solution in H k (k ≥ 2) has been obtained; due to partial dissipation and strong nonlinearity, the global well-posedness of weak solution in H 1 is still unknown. In this paper, by combining classic Galerkin's method with Brouwer's fixed point theorem, existence of time-periodic solution in H 1 with small initial values is obtained. [ABSTRACT FROM AUTHOR]