Your conjecture appears to be true. Here's a visual approach:
Show[Plot[{-Sqrt[u^3], Sqrt[u^3]}, {u, 0, 2}, PlotStyle -> Red,
Filling -> {1 -> {{2}, {LightRed, Transparent}}}, Frame -> True],
ContourPlot[expression1[u, v], {u, 0, 2}, {v, -Sqrt[8], Sqrt[8]}, PlotRange -> All,
Contours -> 20, ContourLabels -> True, ContourShading -> None]
]
