Global existence of the radially symmetric solutions of the Navier-Stokes equations for the isentropic compressible fluids

We study the isentropic compressible Navier-Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non-negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ₀, u₀ satisfy the compatibility condition -μΔu₀ - (λ + μ) ∇ div u₀ + ∇(Aρ₀^γ) = ρ₀^1/2g for some radially symmetric g ∈ L ². The initial density ρ₀ needs not be positive. We also prove some uniqueness results on the strong solutions.