Global Classical Solutions Of The Full Compressible Navier-stokes Equations With Cylindrical Or Spherical Symmetry

In this paper,we consider the full compressible Navier-Stokes Equations in N(N?2)space dimensional with cylindrically or spherically symmetric initial data.The global existence of strong and classical solutions are established.The analysis is based on some delicate a priori estimates which depend on the assumption ?(?)= ?q where q ? 0 and(p0,?0)? H2,(u0,v0,w0)? H01 ? H2.Compared with the results in Wen and Zhu(2014)and Qin,Yang,Yao and Zhou(2015),our results relax the restriction q>0,when there is no initial vacuum and include the global existence of classical solutions for both the cylindrically or spherically symmetric cases,respectively.It should be point out that we obtain the global classical solutions with the help of weighted H3 estimates of(u,v,w,?).In Chapter 1,we introduce the progress of the well-posedness theory of the full compressible Navier-Stokes equations both at home and abroad.In Chapter 2,we consider the exsitence of strong solutions for the full com-pressible Navier-Stokes Equations.Specifically,we get the existence of global strong solutions,when we assume that ?(?)=?q,q?0.In Chapter 3,we consider the exsitence of classical solutions for the full compressible Navier-Stokes Equations.Specifically,we get the existence of global classical solutions,by the weighted estimates of(t2/1u,t2/1,t2/1w,t2/1?).