Add a comma after align numeration in Latex

Question

My problem is that I want to add a coma at the end of each equation/row in my set of equations in the align environnement.

Here is my set of equations:

\begin{align}
\frac{\partial h}{\partial t}+\frac{\partial(uh)}{\partial x}+\frac{\partial (vh)}{\partial y}&= e_wU -V_s \\
\frac{\partial (uh)}{\partial t} + \frac{\partial (u^2h+\frac{g'}{2}h^2)}{\partial x}+\frac{\partial (uvh)}{\partial y} &= +g'hS_x-\frac{\tau_{b_x}}{\rho_{eau}}+f_{corr}hv \\
\frac{\partial (vh)}{\partial t} + \frac{\partial (v^2h+\frac{g'}{2}h^2)}{\partial y}+\frac{\partial (uvh)}{\partial x} &= +g'hS_y-\frac{\tau_{b_y}}{\rho_{eau}}-f_{corr}hu \\
\frac{\partial (C_ih)}{\partial t} + \frac{\partial (uC_ih)}{\partial x}+\frac{\partial (vC_ih)}{\partial y} &= E_i-D_i\\
(1-\varphi)\frac{\partial \eta}{\partial t} &= D_{tot}-E_{tot}
\end{align}

Answer 1

If you want your comma (or full stop) at the end of the equation, I see no other solution than doing it manually, maybe following a small space like \,:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
     \frac{\partial h}{\partial t}+\frac{\partial(uh)}{\partial x}+\frac{\partial (vh)}{\partial y}&= e_wU -V_s\,,\\
     \frac{\partial (uh)}{\partial t} + \frac{\partial (u^2h+\frac{g'}{2}h^2)}{\partial x}+\frac{\partial (uvh)}{\partial y} &= +g'hS_x-\frac{\tau_{b_x}}{\rho_{eau}}+f_{corr}hv\,,\\
     \frac{\partial (vh)}{\partial t} + \frac{\partial (v^2h+\frac{g'}{2}h^2)}{\partial y}+\frac{\partial (uvh)}{\partial x} &= +g'hS_y-\frac{\tau_{b_y}}{\rho_{eau}}-f_{corr}hu\,,\\
     \frac{\partial (C_ih)}{\partial t} + \frac{\partial (uC_ih)}{\partial x}+\frac{\partial (vC_ih)}{\partial y} &= E_i-D_i\,,\\
     (1-\varphi)\frac{\partial \eta}{\partial t} &= D_{tot}-E_{tot}\,.
\end{align}

\end{document}

---

Instead, if you want punctuation after the equation number, you can use the command \tag*{} with an argument like (1),, (2). or so:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
     \frac{\partial h}{\partial t}+\frac{\partial(uh)}{\partial x}+\frac{\partial (vh)}{\partial y}&= e_wU -V_s \tag*{(1),}\\
     \frac{\partial (uh)}{\partial t} + \frac{\partial (u^2h+\frac{g'}{2}h^2)}{\partial x}+\frac{\partial (uvh)}{\partial y} &= +g'hS_x-\frac{\tau_{b_x}}{\rho_{eau}}+f_{corr}hv  \tag*{(2),}\\
     \frac{\partial (vh)}{\partial t} + \frac{\partial (v^2h+\frac{g'}{2}h^2)}{\partial y}+\frac{\partial (uvh)}{\partial x} &= +g'hS_y-\frac{\tau_{b_y}}{\rho_{eau}}-f_{corr}hu  \tag*{(3),}\\
     \frac{\partial (C_ih)}{\partial t} + \frac{\partial (uC_ih)}{\partial x}+\frac{\partial (vC_ih)}{\partial y} &= E_i-D_i \tag*{(4),}\\
     (1-\varphi)\frac{\partial \eta}{\partial t} &= D_{tot}-E_{tot} \tag*{(5).}
\end{align}

\end{document}

To implement this globally in your document(s), editing some lower level TeX code may be necessary or at least recommended.