Global Stability of Large Solutions to the 3D Compressible Navier-Stokes Equations
Global Stability of Large Solutions to the 3D Compressible Navier-Stokes Equations
复制标题
3D可压缩纳维-斯托克斯方程大解的全局稳定性
DOI：
10.1007/s00205-019-01410-8
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发表时间：
2019
影响因子：
2.5
通讯作者：
Wang Chao
中科院分区：
文献类型：
--
作者：
He Lingbing;Huang Jingchi;Wang Chao
本文研究了全空间可压缩N-S方程大解的全局稳定性。我们的主要结果和创新之处在于：在密度可验证且任意小的假设下，我们建立了一种新的方法，以与热方程相同的显式衰减率收敛到与其相关的平衡点。证明的主要思想依赖于基本能量恒等式、爆破准则的技巧和对解的低频部分的新估计，证明了方程的全局时间稳定性，即任何摄动解都将保持接近参考解，如果它们最初彼此接近。在Paicuant和Zhang(J Funct Anal 262(8)：3556-3584,2012)的启发下，我们构造了一类初始数据为内型临界空间且远离平衡的方程的整体大解。这里，“大解”是指速度的不可压缩部分的垂直分量可以任意大。
The present paper investigates the global stability of large solutions to the compressible Navier–Stokes equations in the whole space. Our main results and innovations can be stated as follows:Under the assumption that the densityverifiesandwitharbitrarily small, we establish a new approach for the convergence of the solutions to its associated equilibrium with an explicit decay rate which is the same as that for the heat equation. The main idea of the proof relies on the basic energy identity, techniques from blow-up criterion and a new estimate for the low frequency part of the solutions.We prove the global-in-time stability for the equations, i.e, any perturbed solutions will remain close to the reference solutions if initially they are close to one another. This implies that the set of the smooth and bounded solutions is open.Inspired byPaicuandZhang(J Funct Anal 262(8):3556–3584, 2012), we construct global large solutions to the equations with a class of initial data which are intype critical spaces and far away from equilibrium. Here, “large solutions” means that the vertical component of the incompressible part of the velocity could be arbitrarily large.