
Here we analyze NavierStokes equations,
which govern the behavior of viscous incompressible flows:
These equations can be rewritten in a dimensionless form:
where
is known as the flow Reynolds number.
Solving these equations shows mainly two difficulties:

Nonlinear convective terms 

Stabilized formulations have to be used to ensure
a stable solution when dealing with high Reynolds number flows.


Incompressibility constraint 

The unknowns (velocity and pressure) cannot be discretized anyhow.
Solution is guaranteed if interpolation spaces verify a stability condition
known as infsup or LBB condition.

Besides, when the unsteady case is considered, we have to find
proper techniques to trace the transient solution.

