You cannot use expressions with persp, ... a well documented limitation. The usual advice is to switch to lattice:
library(lattice)
png(); print( wireframe(z_1~x+y ,data=data.frame(x=x, y=rep(y, each=length(x)), z_1=z_1) ,
xlab=expression(u[1]), ylab=expression(u[2]), zlab = "Z") ); dev.off()