@Article{JPDE-10-158,
author = {Huaiyu Jian },
title = {Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations},
journal = {Journal of Partial Differential Equations},
year = {1997},
volume = {10},
number = {2},
pages = {158--168},
abstract = { 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)},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5589.html}
}