On Spherically Symmetric Solutions¶of the Compressible Isentropic Navier–Stokes Equations
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We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier–Stokes equations in ℝ n (n= 2, 3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new (multidimensional) property induced by the viscous flux. The present paper extends Lions' existence theorem  to the case 1< γ <γ n for spherically symmetric initial data, where γ is the specific heat ratio in the pressure, γ n = 3/2 for n= 2 and γ n = 9/5 for n= 3.
Dedicated to Professor Rolf Leis on the occasion of his 70th birthday
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