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[tex]\frac{\partial \rho}{\partial t}=\frac{\partial v_1\rho}{\partial x_1}+\frac{\partial v_2\rho}{\partial x_2}[/tex]

for v_1 = -x_2 and v_2=x_1

i obtain equation

[tex]\frac{\partial \rho}{\partial t}+x_2\frac{\partial\rho}{\partial x_1}-x_1\frac{\partial \rho}{\partial x_2}=0[/tex]

Charakteristik system is

[tex]\begin{array}{rcl}t'&=&1\\x_1'&=&x_2\\x_2'&=&-x_1\end{array}[/tex]

Thanks