This is the first note for my Jianshu
Today I am writing my PhD. thesis, the motivation part is really difficult to write, seems the topic for me is not so that meaningful ...
I want to try whether the latex equation function works in Jianshu, but I forget the syntax of MD
$$
\frac{\partial \mathbf{q}}{\partial t} + \frac{\partial \mathbf{f}}{\partial x}+ \frac{\partial \mathbf{g}}{\partial y} = \mathbf{s}
$$
with vectors defined as
$$
\begin{equation}
\mathbf{q} = \begin{bmatrix}
h\
q_{x}\
q_{y}
\end{bmatrix}, \quad \mathbf{f} = \begin{bmatrix}
q_{x}\
u q_{x} + gh^{2}/2\
u q_{y}
\end{bmatrix}, \quad
\mathbf{g} = \begin{bmatrix}
q_{y}\
v q_{x}\
v q_{y} + gh^{2}/2
\end{bmatrix},
\end{equation}
$$
$$
\begin{equation}
\mathbf{s} = \begin{bmatrix}
s_h\
-g h \frac{ \partial z}{ \partial x} - c_{f} u \sqrt{u^{2} + v^{2}} + s_{e_x}\
-g h \frac{ \partial z}{ \partial y} - c_{f} v \sqrt{u^{2} + v^{2}} + s_{e_y}
\end{bmatrix},
\end{equation}
$$
