Undefined control sequence. end{align*}

Well, assuming that you defined some commands somewhere in your document, I took the liberty to define them too to be able to compile your document.

The problems were:

1. All the user-undefined commands. I created them but you'll have to change to the correct ones later.

2. The align* environment produces an unnumbered equation, so you cannot put labels in it (unless you have a tag on that same line, as barbara beeton says).

After some modifications, here is your code, with only the amsmath package and your mysterious user-defined commands.

I also added another version where you can put labels on your equations.

documentclass{article}
usepackage{amsmath}
begin{document}
newcommand{DIV}{div}
newcommand{BP}{left<BPright>}
newcommand{Bzero}{left<Bzeroright>}
newcommand{BQ}{left<BQright>}
newcommand{p}{left<pright>}
newcommand{BF}{left<BFright>}

begin{align*}
    DIV BP & = Bzero~,
    rho_0 c dot{theta} & = -DIV BQ + thetap{theta}BP:dot{BF}~.
end{align*}

begin{subequations}
 begin{align}
    DIV BP & = Bzero~,label{PDE1}
    rho_0 c dot{theta} & = -DIV BQ + thetap{theta}BP:dot{BF}~.label{PDE2}
 end{align}
end{subequations}

See Eqs. ref{PDE1} and ref{PDE2}

end{document}