definition of a smooth scalar potential

Question

Have been asked to show that any flow described by a smooth scalar potential is irrotational. I know to show if a flow is irrotational curl of q = 0. But not too sure what is meant by smooth scalar potential. Is it just showing the scalar potential X grad = 0??

any helps super appreiciated!!!

Answer 1

The potential $\phi$ is smooth. The flow $v=\nabla \phi$ is smooth as well. You have to show that curl$v = $curl$ \nabla \phi=0$.