Global Existence Of Spherically Symmetric Solutions For A Nonlinear Compressible Navier-Stokes Equations

In this paper we discuss the global existence of solutions for the nonlinear compressible Navier-Stokes equations with external forces and initial-boundary conditions. I.e., when the external forces f(∫₀^x udy,t)≠0, g(∫₀^x udy,t)≠0, (x,t)∈[0,L]×[0,∞) and f(∫₀^x udy, t)≠const, g(∫₀^x udy, t)≠const, equations: u_t-(r^n-1v)_x=0, v_t-r^n-1(β(r^n-1v)x/u-Rθ/u)x=f(∫₀^x udy,t), C_vθ_t-k(r^2n-2θ_x/u)x-1/u(β(r^n-1v)x-Rθ](r^n-1v)x+2μ(n-1)(r^n-2v²)_x²=g(∫_<sup>x₀ udy, t). With initial-boundary conditions. We will show the global existence of solutions in space H¹, H², H⁴.This paper has four part: chapter one is introduction, involve the model we investigated, the results correlation this paper, and denotations we used; Chapter two to chapter four is the important content, involve the theorems and proves.The new results we have are four aspects: 1, the solution u has uniform positive lower and upper bounds. 2, the global existence of solutions in space H¹. 3, the global existence of solutions in space H². 4, the global existence of solutions in space H⁴.The main difference between this paper and others is the externat forces. This paper applied energy method, by some important inequalities, obtained a uniform priori estimates, finally gained the results.