Table 5.

Example 3.5: Navier–Stokes, low Reynolds number. Note that −Δv=u. In the first column, the Reynolds number is chosen to be small enough so that the dynamics are dominated by viscous flow. The coefficients in the first column show that the method identifies the viscous flow model, which is the true dominant behaviour of the data. The coefficients are within 1% of the true value.

terms	$Re=\frac{1}{10}$, noise=56.0%	Re=4, noise=56.8%	Re=100, noise=60.4%
u	0	0	0
u2	0	0	0
u3	0	0	0
ux	0	0	0
uy	0	0	0
$u_x^2$	0	0	0
$u_y^2$	0	0	0
uyux	0	0	0
vxux	0	0	0
vyux	0	−1.0047	−1.0004
vxuy	0	1.0057	1.0006
vyuy	0	0	0
uxx	0	0	0
uyy	0	0	0
uxy	0	0	0
Δu	10.0563	0.2513	0.0101
Δ2u	0	0	0