From debb75b90b5b37114e1282caa540790c5ac70638 Mon Sep 17 00:00:00 2001
From: "Claudius \"keldu\" Holeksa" <mail@keldu.de>
Date: Mon, 10 Nov 2025 17:28:54 +0100
Subject: Commit this I guess?

---
 typst/report.typ | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/typst/report.typ b/typst/report.typ
index 8f16f96..112ed12 100644
--- a/typst/report.typ
+++ b/typst/report.typ
@@ -17,25 +17,37 @@ For the understanding of near-well injections multiple elements such as multipha
 the geometry of the porous structure is required.  
 While at heart most numerical modelling approaches such as the Lattice-Boltzmann-Method are based on the Navier-Stokes Equations,
 here we will take a glance on a more special case.  
-Since we are interested in very viscous cases with our Reynolds number (Re<<1) our base equation reduces itself to the Stokes Equations,
+Since we are interested in very viscous cases with our Reynolds number (Re \< \< 1) our base equation reduces itself to the Stokes Equations,
 which are well understand in terms of the description by Stokes [dummy, I mean the old paper from 1851].
 So the Navier-Stokes equations
 
-@todo insert NS eqs here
+todo insert NS eqs here
 
 are reduced to
 
-@todo insert S eqs here
+todo insert S eqs here
 // Rather move this to the lower chapters and use book citations I guess. Well, maybe also Stokes paper. The initial rant is quite fun
 
 
 == Navier
 
+The Navier Stokes equations are governed as follows
+
+// we don't really need the external force here? do we?
+
+#math.equation(
+block: true,
+$ ρ((∂)/(∂t)u + (u · ∇)u) = −∇p + μ∇²u + f\
+∇ · u = 0 $
+)
+
 // Introduction
 == Stokes flow
 
+While we are often interested in Navier-Stokes flows, on higher viscous fluids the viscosity dominates.
+
 
-== Solid-Fluid interaction
+== Solid-Fluid interaction with Stokes flow
 
 So while
 
-- 
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