Example of $v(x,y)$ and $w(x,y)$ with $\frac{\partial v}{\partial x} + \frac{\partial w}{\partial y} = 0$ and they are zero on $xy(1-x)(1-y) = 0$

Question

This problem occured because of Stokes inequality.

I'm interested in functions, for which $v(x,0) = v(x,1) = v(0,y) = v(1,y) = 0 = w(0,y) = w(1,y) = w(x,0)=w(x,1)$ and $\frac{\partial v}{\partial x} + \frac{\partial w}{\partial y} = 0$ inside $\{0 < x < 1, 0 < y < 1\}$.

I've tried to construct them, but there is a problem with bounds.