  We study the well-posedness of radial solutions for general nonlinear
hyperbolic systems in three dimensions. We give a proof of the global existence
of radial solutions for general semilinear hyperbolic systems in 3D under null
condition, with small scaling invariant $\dot{W}^{2,1}(\mathbb{R}^3)$ data. We
obtain a bilinear estimate that is effective to the hyperbolic systems which do
not have any time decay. It allows us to achieve the boundedness of the
weighted BV norm of the radial solution.
