Global Spherically Symmetric Solutions To The Full Compressible Navier-stokes Equations With Density And Temperature Dependent Transport Coefcients In An Annular Domain

This paper is concerned with the global existence of spherically symmetric so-lution to the initial-boundary value problems of the2-dimensional full compressibleNavier-Stokes equations with density and temperature dependent transport coefcientsin an annular domain. First, We rewrite the Navier-Stokes equations in a sphericallysymmetric form, then transfer the resulting equations into the corresponding form ofin Lagrangian coordinate. We obtain the global existence of strong solution based onthe continuation arguments with a combination of the local existence theorem with apriori estimates of strong solution. The key parts in this thesis are to derive the a prioriestimates of strong solutions. Under the main assumptions that the viscosity coef-cients and the coefcient of heat conductivity depend on density and temperature, wecan show vacuum never happens provided that the initial density has no vacuum, thenwe can derive the required a priori estimate in the Sobolev space Hs(s≥3).