Optimal control of a free particle

Question

I want to take to $(0,0)$ in least time the system $$\dot{x}(t)=y(t),\quad \dot{y}(t)=u(t),\quad x(0)=x_0,\ y(0)=y_0$$ where $|u|\leq1$. I already did this via Pontryaguin, but I couldn't do via Hamilton Jacobi. How can I state the problem even? Is the solution smooth? aaa