How to add an empty line between two formulars

I have the following code

\listfiles
\documentclass[oneside,12pt]{scrartcl}
\usepackage[ngerman]{babel}
%\usepackage{amsmath}
\usepackage[fixamsmath,disallowspaces]{mathtools}
\begin{document}

\underline{Verschiebare Ger{\"a}te}

\begin{math}
P_j(t,s_j) = \begin{cases}
0 & \text{for } t < s_j \\
Q_j(t-s_j) & \text{for  }s_j \leq t\leq s_j+p_j  \\
0 & \text{for  } t>s_j+p_j
\end{cases}
\end{math}

\newline

\begin{math}
\text{with }s_j = r_j+ \Delta t\\
\Delta t\leq tDoF
\end{math}

\end{document}

And I would like to add an empty line between the two math-parts. Unfortunately the command \newline or \\ does not work in this context. Can you help me?

math is the same as \( or \$ and designed for inline math not displays. You want a display environment such as equation or align that will automatically offset the expression with vertical space and not require forced adjustments, for example:

\documentclass[oneside,12pt]{scrartcl}
\usepackage[ngerman]{babel}
%\usepackage{amsmath}
\usepackage[fixamsmath,disallowspaces]{mathtools}
\begin{document}

\section*{Verschiebare Ger{\"a}te}

\begin{equation*}
P_j(t,s_j) = \begin{cases}
0 & \text{for } t < s_j \\
Q_j(t-s_j) & \text{for  }s_j \leq t\leq s_j+p_j  \\
0 & \text{for  } t>s_j+p_j
\end{cases}
\end{equation*}
with
\begin{align*}
s_j = r_j+ \Delta t\\
\Delta t\leq tDoF
\end{align*}

\end{document}