Optimal decay rates on compressible Navier-Stokes equations with degenerate viscosity and vacuum
Optimal decay rates on compressible Navier-Stokes equations with degenerate viscosity and vacuum
复制标题
具有简并粘度和真空的可压缩纳维-斯托克斯方程的最优衰减率
DOI：
10.1016/j.matpur.2019.01.014
复制
发表时间：
2019
影响因子：
2.3
通讯作者：
Zhu Changjiang
中科院分区：
文献类型：
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作者：
Hong Guangyi;Zhu Changjiang
这是论文[16，Math. Models Methods Appl.Sci. 28（2018）337-386]关于具有退化粘性和真空的一维等熵可压缩Navier-Stokes方程自由边界问题弱解的大时间行为的研究。在初始数据（初始能量）的适当小条件下，推广了[16，Math. Models Methods Appl.Sci. 28（2018）337-386]的情况下，γ> 1和θ< min {1，γ− 1 2}。显然，研究了密度函数沿着的最佳衰减率及其在界面附近的行为。同时，我们也得到了更尖锐的衰减率的范数的速度函数。证明是基于标准线方法。关键是建立一些新的全局时间加权（在时间和空间）估计一致的真空边界，这将确保一致收敛的近似解。
This is a continuation of the paper [16, Math. Models Methods Appl. Sci. 28 (2018) 337–386] on the study of the large time behavior of the weak solution to the free boundary problem for one-dimensional isentropic compressible Navier–Stokes equations with degenerate viscosity and vacuum. Under appropriate smallness conditions on the initial data (initial energy), we extend the results in [16, Math. Models Methods Appl. Sci. 28 (2018) 337–386] to the case γ> 1 and θ< min{1, γ− 1 2}. Clearly, the optimal decay rate of the density function along with its behavior near the interfaces is studied. In the meanwhile, we obtain also sharper decay rates for the norms in terms of the velocity function. The proof is based on the standard line method. The key is to establish some new global-in-time weighted (both in time and space) estimates uniformly up to the vacuum boundary, which ensures the uniform convergence of the approximate solutions.