The article is devoted to the study of isentropic approximation and Gevrey regularity for the full compressible Euler system in \({\mathbb {R}}^{N}\) (or \({\mathbb {T}}^{N}\)) with any dimension \(N\ge 1\). We first establish the existence and uniqueness of solution in Gevrey function spaces \(G_{\sigma ,s}^{r}({\mathbb {R}}^{N})\), 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 \(G_{\sigma ,s}^{r}({\mathbb {R}}^{N})\). Finally, the isentropic approximation is investigated in Banach spaces \({\mathcal {B}}_{T}^\nu ({\mathbb {R}}^{N})\), provided the initial entropy \(S_{0}(x)\) changes closing a constant \({\bar{S}}\) in Gevrey function spaces \(G_{\sigma ,s}^{r}({\mathbb {R}}^{N})\).

本文专门研究\（{\ mathbb {R}} ^ {N} \）（或\（{\ mathbb {T}} ^ {N} \））任何尺寸\（N \ ge 1 \）。我们首先在Gevrey函数空间\（G _ {\ sigma，s} ^ {r}（{\ mathbb {R}} ^ {N}）\）中建立解的存在性和唯一性，然后用连续性的定义模量，我们证明了Euler系统的解连续依赖于\（G _ {\ sigma，s} ^ {r}（{\ mathbb {R}} ^ {N}）中的初始数据\ {v_ {0} \ ） \）。最后，在Banach空间\（{\ mathcal {B}} _ {T} ^ \ nu（{\ mathbb {R}} ^ {N}）\）中研究等熵近似，所提供的初始熵\（S_ {0}（X）\）改变关闭恒定\（{\巴{S}} \）中的Gevrey函数空间\（G _ {\ SIGMA，S} ^ {R}（{ \ mathbb {R}} ^ {N}）\）。