Solution
= Solution
Use the <stream function> convention $u=\psi_y$, $v=-\psi_x$. It gives $u=-\sin x\sin y$, $v=-\cos x\cos y$. Then
$$
u_x+v_y=-\cos x\sin y+\cos x\sin y=0,
$$
so \b[the flow is incompressible].
= Solution
Use the <stream function> convention $u=\psi_y$, $v=-\psi_x$. It gives $u=-\sin x\sin y$, $v=-\cos x\cos y$. Then
$$
u_x+v_y=-\cos x\sin y+\cos x\sin y=0,
$$
so \b[the flow is incompressible].