I am trying to out my boundary conditions in curly brackets but have got errors

Question

I am currently conducting research on the solar wind and need to include boundary conditions in my paper. I have used the following:

\usepackage{amsmath,cases}
\begin{numcases}{}
    $ T(r_{0})=T_{0} $ &  \\
    $ T\xrightarrow{}0 $ & \text{for $r\xrightarrow{}\infty $}
\end{numcases}

Which produces what I would like but I get errors for these lines, shown in the image. I am unsure how to correct these, any advice would be welcome.

Answer 1

the first column in numcases is in math node, the socond in "text" mode. consequently all$ in the first column should be removed:

\documentclass{article}
\usepackage{amsmath,cases}
    \begin{document}
\begin{numcases}{}
T(r_{0})=T_{0}      &  \\
T\xrightarrow{}0    & for $r\rightarrow\infty $
\end{numcases}
    \end{document}

Answer 2

JUst to point the same result can be obtained with empheq (which loads mathtools, hence amsmath), with more control on the layout:

\documentclass{article}
\usepackage{empheq}

\begin{document}

\begin{empheq}[left = \empheqlbrace]{alignat = 2}
 & T(r_{0})=T_{0}, & \\
 & T\xrightarrow{}0 &\quad & \text{for } r \rightarrow \infty
\end{empheq}
\bigskip

or even :
\setcounter{equation}{0}
\begin{subequations}
  \begin{empheq}[left = \empheqlbrace]{alignat = 2}
 & T(r_{0})=T_{0}, & \\
 & T\xrightarrow{}0 &\quad & \text{for } r \rightarrow \infty
\end{empheq}
\end{subequations}

\end{document}