论文标题
大型解决方案的稳定性，用于整个空间中完全可压缩的Navier-Stokes方程
Stability of large solutions for full compressible Navier-Stokes equations in the whole spaces
论文作者
论文摘要
当前的论文致力于调查整个空间中整个Navier-Stokes-foury System的大型解决方案的全球时间稳定性。假设密度和温度在持有人空间中均匀地从上方界定，$ c^α$，$α$分别很小，分别在$ l^\ infty $空间中。然后我们证明了两个结果：（1）。如果我们对初始数据强加相同的条件，则这种解决方案将以与热方程相同的速率收敛到其相关的平衡。结果，我们获得了密度和温度的正下限的传播。 （2）。这种解决方案是稳定的，也就是说，如果最初它们彼此靠近，则任何扰动的解决方案都将保持靠近参考解决方案。这表明平滑和有限的解决方案的集合是打开的。
The current paper is devoted to the investigation of the global-in-time stability of large solutions for the full Navier-Stokes-Fourier system in the whole space. Suppose that the density and the temperature are bounded from above uniformly in time in the Holder space $C^α$ with $α$ sufficiently small and in $L^\infty$ space respectively. Then we prove two results: (1). Such kind of the solution will converge to its associated equilibrium with a rate which is the same as that for the heat equation if we impose the same condition on the initial data. As a result, we obtain the propagation of positive lower bounds of the density and the temperature. (2). Such kind of the solution is stable, that is, any perturbed solution will remain close to the reference solution if initially they are close to each other. This shows that the set of the smooth and bounded solutions is open.
