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diff --git a/source/know/concept/prandtl-equations/index.md b/source/know/concept/prandtl-equations/index.md
index 3afe405..d82657c 100644
--- a/source/know/concept/prandtl-equations/index.md
+++ b/source/know/concept/prandtl-equations/index.md
@@ -11,7 +11,7 @@ layout: "concept"
 
 In fluid dynamics, the **Prandtl equations** or **boundary layer equations**
 describe the movement of a [viscous](/know/concept/viscosity/) fluid
-with a large [Reynolds number](/know/concept/reynolds-number/) $\mathrm{Re} \gg 1$
+with a large [Reynolds number](/know/concept/reynolds-number/) $$\mathrm{Re} \gg 1$$
 close to a solid surface.
 
 Fluids with a large Reynolds number
@@ -27,23 +27,23 @@ where viscosity plays an important role.
 This is in contrast to the ideal flow far away from the surface.
 
 We consider a simple theoretical case in 2D:
-a large flat surface located at $y = 0$ for all $x \in \mathbb{R}$,
-with a fluid *trying* to flow parallel to it at $U$.
-The 2D treatment can be justified by assuming that everything is constant in the $z$-direction.
+a large flat surface located at $$y = 0$$ for all $$x \in \mathbb{R}$$,
+with a fluid *trying* to flow parallel to it at $$U$$.
+The 2D treatment can be justified by assuming that everything is constant in the $$z$$-direction.
 We will not solve this case,
 but instead derive general equations
 to describe the flow close to a flat surface.
 
-At the wall, there is a very thin boundary layer of thickness $\delta$,
-where the fluid is assumed to be completely stationary $\va{v} = 0$.
-We are mainly interested in the region $\delta < y \ll L$,
-where $L$ is the distance at which the fluid becomes practically ideal.
+At the wall, there is a very thin boundary layer of thickness $$\delta$$,
+where the fluid is assumed to be completely stationary $$\va{v} = 0$$.
+We are mainly interested in the region $$\delta < y \ll L$$,
+where $$L$$ is the distance at which the fluid becomes practically ideal.
 This the so-called **slip-flow** region,
 in which the fluid is not stationary,
 but still viscosity-dominated.
 
 In 2D, the steady Navier-Stokes equations are as follows,
-where the flow $\va{v} = (v_x, v_y)$:
+where the flow $$\va{v} = (v_x, v_y)$$:
 
 $$\begin{aligned}
     v_x \pdv{v_x}{x} + v_y \pdv{v_x}{y}
@@ -58,10 +58,10 @@ $$\begin{aligned}
 
 The latter represents the fluid's incompressibility.
 We non-dimensionalize these equations,
-and assume that changes along the $y$-axis
-happen on a short scale (say, $\delta$),
-and along the $x$-axis on a longer scale (say, $L$).
-Let $\tilde{x}$ and $\tilde{y}$ be dimenionless variables of order $1$:
+and assume that changes along the $$y$$-axis
+happen on a short scale (say, $$\delta$$),
+and along the $$x$$-axis on a longer scale (say, $$L$$).
+Let $$\tilde{x}$$ and $$\tilde{y}$$ be dimenionless variables of order $$1$$:
 
 $$\begin{aligned}
     x
@@ -106,7 +106,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 For future convenience,
-we multiply the former equation by $L / U^2$, and the latter by $\delta / U^2$:
+we multiply the former equation by $$L / U^2$$, and the latter by $$\delta / U^2$$:
 
 $$\begin{aligned}
     \tilde{v}_x \pdv{\tilde{v}_x}{\tilde{x}} + \tilde{v}_y \pdv{\tilde{v}_x}{\tilde{y}}
@@ -118,12 +118,12 @@ $$\begin{aligned}
     + \nu \Big( \frac{\delta^2}{U L^3} \pdvn{2}{\tilde{v}_y}{\tilde{x}} + \frac{1}{U L} \pdvn{2}{\tilde{v}_y}{\tilde{y}} \Big)
 \end{aligned}$$
 
-We would like to estimate $\delta$.
-Intuitively, we expect that higher viscosities $\nu$ give thicker layers,
-and that faster velocities $U$ give thinner layers.
+We would like to estimate $$\delta$$.
+Intuitively, we expect that higher viscosities $$\nu$$ give thicker layers,
+and that faster velocities $$U$$ give thinner layers.
 Furthermore, we expect *downstream thickening*:
-with distance $x$, viscous stresses slow down the slip-flow,
-leading to a gradual increase of $\delta(x)$.
+with distance $$x$$, viscous stresses slow down the slip-flow,
+leading to a gradual increase of $$\delta(x)$$.
 Some dimensional analysis thus yields the following estimate:
 
 $$\begin{aligned}
@@ -132,7 +132,7 @@ $$\begin{aligned}
     \sim \sqrt{\frac{\nu L}{U}}
 \end{aligned}$$
 
-We thus insert $\delta = \sqrt{\nu L / U}$ into the Navier-Stokes equations, giving us:
+We thus insert $$\delta = \sqrt{\nu L / U}$$ into the Navier-Stokes equations, giving us:
 
 $$\begin{aligned}
     \tilde{v}_x \pdv{\tilde{v}_x}{\tilde{x}} + \tilde{v}_y \pdv{\tilde{v}_x}{\tilde{y}}
@@ -144,7 +144,7 @@ $$\begin{aligned}
     + \nu \Big( \frac{\nu}{U^2 L^2} \pdvn{2}{\tilde{v}_y}{\tilde{x}} + \frac{1}{U L} \pdvn{2}{\tilde{v}_y}{\tilde{y}} \Big)
 \end{aligned}$$
 
-Here, we recognize the definition of the Reynolds number $\mathrm{Re} = U L / \nu$:
+Here, we recognize the definition of the Reynolds number $$\mathrm{Re} = U L / \nu$$:
 
 $$\begin{aligned}
     \tilde{v}_x \pdv{\tilde{v}_x}{\tilde{x}} + \tilde{v}_y \pdv{\tilde{v}_x}{\tilde{y}}
@@ -156,8 +156,8 @@ $$\begin{aligned}
     + \frac{1}{\mathrm{Re}^2} \pdvn{2}{\tilde{v}_y}{\tilde{x}} + \frac{1}{\mathrm{Re}} \pdvn{2}{\tilde{v}_y}{\tilde{y}}
 \end{aligned}$$
 
-Recall that we are only considering large Reynolds numbers $\mathrm{Re} \gg 1$,
-in which case $\mathrm{Re}^{-1} \ll 1$,
+Recall that we are only considering large Reynolds numbers $$\mathrm{Re} \gg 1$$,
+in which case $$\mathrm{Re}^{-1} \ll 1$$,
 so we can drop many terms, leaving us with these redimensionalized equations:
 
 $$\begin{aligned}
@@ -168,11 +168,11 @@ $$\begin{aligned}
     = 0
 \end{aligned}$$
 
-The second one tells us that for a given $x$-value,
+The second one tells us that for a given $$x$$-value,
 the pressure is the same at the surface
-as in the main flow $y > L$, where the fluid is ideal.
-In the latter regime, we apply Bernoulli's theorem to rewrite $p$,
-using the *Bernoulli head* $H$ and the mainstream velocity $U(x)$:
+as in the main flow $$y > L$$, where the fluid is ideal.
+In the latter regime, we apply Bernoulli's theorem to rewrite $$p$$,
+using the *Bernoulli head* $$H$$ and the mainstream velocity $$U(x)$$:
 
 $$\begin{aligned}
     p