Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations

Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞≤(2+1/N)‖divu‖L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.