TY - JOUR
T1 - Global Smooth Solutions to a System of Dissipative Nonlinear Evolution Equations
AU - Huaiyu Jian 
JO - Journal of Partial Differential Equations
VL - 2
SP - 158
EP - 168
PY - 1997
DA - 1997/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5589.html
KW - System of parabolic equations
KW - nonlinear
KW - initial-boundary problem
KW - global classical solution
AB -  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)