Corrected typos

lattice-boltzmann.com/content/1-dimensionless-lbm.md

@@ -25,7 +25,7 @@ $$
 &\partial_t\bm{u}+\bm{u}\cdot\bm{\nabla}\bm{u}=-\frac{1}{\rho}\bm{\nabla}p+\nu\bm{\nabla}^2\bm{u},
 \end{align}
 $$
-where $p$, $\rho$, $\nu$, and $\bm{u}$ are respectively the pressure, density, kinematic viscosity, and velocity of the flow.
+where $p$, $\rho$ (which is a constant in the incompressible model), $\nu$, and $\bm{u}$ are respectively the pressure, density, kinematic viscosity, and velocity of the flow.
 
 In order to transform this equation into its dimensionless form a certain amount of characteristic lengths calves must be chosen. Here we will define $U$ as the characteristic velocity of the flow and $L$ its characteristic length.
 
@@ -56,7 +56,7 @@ $$
 \begin{aligned}
 &\bm{u}^\ast=\frac{L}{\nu}\bm{u}, &p^\ast=\frac{L^2}{\nu^2\rho}p,\\\\
 &t^\ast=\frac{\nu}{L^2}t, &\bm{x}^\ast=\frac{\bm{x}}{L},\\\\
-&\frac{\partial}{\partial t^\ast}=\frac{L^2}{\nu}\frac{\partial}{\partial t}, &\bm{\nabla}^\ast=L\bm{\nabla}
+&\partial_t^\ast=\frac{L^2}{\nu}\partial_t, &\bm{\nabla}^\ast=L\bm{\nabla}
 \end{aligned}
 \end{equation}
 $$
@@ -108,7 +108,7 @@ $$
 \begin{aligned}
 &\bm{\xi}^\ast=\frac{1}{\xi_0}\bm{\xi},&\quad\rho^\ast=\frac{1}{\rho_0}\rho,\\\\
 &t^\ast=\frac{\xi_0}{L}t,&\quad\bm{x}^\ast=\frac{\bm{x}}{L},\\\\
-&\frac{\partial}{\partial t^\ast}=\frac{L}{\xi}\frac{\partial}{\partial t},&\quad\bm{\nabla}^\ast=L\bm{\nabla},\\\\
+&\partial_t^\ast=\frac{L}{\xi_0}\partial_t,&\quad\bm{\nabla}^\ast=L\bm{\nabla},\\\\
 &f^\ast=\frac{\xi_0^D}{\rho_0}f,&\quad{f^{eq}}^\ast=\frac{\xi_0^D}{\rho_0}f^{eq},
 \end{aligned}
 \end{equation}