Isentropic Approximation and Gevrey Regularity for the Full Compressible Euler Equations in RN

The article is devoted to the study of isentropic approximation and Gevrey regularity for the full compressible Euler system in R-N (or T-N) with any dimension N >= 1. We first establish the existence and uniqueness of solution in Gevrey function spaces G(sigma,s)(r)(R-N), then with the definition modulus of continuity, we show that the solution of Euler system is continuously dependent of the initial data v(0) in G(sigma,s)(r)(R-N). Finally, the isentropic approximation is investigated in Banach spaces B-T(nu) (R-N), provided the initial entropy S-0(x) changes closing a constant (S) over bar in Gevrey function spaces G(sigma,s)(r)(R-N).