(untitled) (Journal of Partial Differential Equations, 1997)
The existence and uniqueness are proved for global classical solutions of the following initial-boundary problem for the system of parabolic equations which is proposed by Hsieh as a substitute for the Rayleigh-Benard equation and can lead to Lorenz equations: ψ_t = -(σ - α)ψ - σθ_x, + αψ_xx θ_t = -(1- β)θ + vψ_x + (ψθ)_x + βθ_xx ψ(0,t) = ψ(1,t) = 0, θ_x(0,t) = θ_x(1,t) = 0 ψ(x,0) = ψ_0(x), θ(x,0) = θ_0(x)