Thank you for your help!
It is not w that you want to be zero, but its gradient:
FindRoot[Grad[w[s, u], {s, u}] == 0, {s, 0}, {u, Pi}]
In this case I would try FindMaximum:
FindMaximum
FindMaximum[w[s, u], {s, .3}, {u, .1}]
For exact symbolic solutions you can use Reduce:
Reduce
Reduce[Grad[Rationalize[w[s, u]], {s, u}] == 0 && -1 < s < 1 && -1 < u < 1, {s, u}, Reals] % // N