论文标题
3D可压缩Navier-Stokes方程的全局强解决方案，具有短脉冲类型初始数据
Global strong solutions of 3D Compressible Navier-Stokes equations with short pulse type initial data
论文作者
论文摘要
短脉冲初始基准提到了半径$δ$的球中支撑的一个基准，并带有幅度$δ^{\ frac12} $，看起来像脉冲。克里斯托杜洛（Christodoulou）最初是为了证明爱因斯坦方程式的黑洞的形成，并为可压缩的欧拉方程捕获了冲击形成。 The aim of this article is to consider the same type initial data, which allow the density of the fluid to have large amplitude $δ^{-\fracαγ}$ with $δ\in(0,1],$ for the compressible Navier-Stokes equations. We prove the global well-posedness and show that the initial bump region of the density with large amplitude will disappear within a very short time. As a consequence, we obtain the global dynamic behavior $ \ | \ nabla u \ | _ {l^1（[[0，\ infty）; l^\ infty）} $的解决方案和有限度。证明的关键成分在于有效粘性通量的新观察结果以及通过拉格朗日坐标对密度的新衰减估计。
Short pulse initial datum is referred to the one supported in the ball of radius $δ$ and with amplitude $δ^{\frac12}$ which looks like a pulse. It was first introduced by Christodoulou to prove the formation of black holes for Einstein equations and also to catch the shock formation for compressible Euler equations. The aim of this article is to consider the same type initial data, which allow the density of the fluid to have large amplitude $δ^{-\fracαγ}$ with $δ\in(0,1],$ for the compressible Navier-Stokes equations. We prove the global well-posedness and show that the initial bump region of the density with large amplitude will disappear within a very short time. As a consequence, we obtain the global dynamic behavior of the solutions and the boundedness of $\|\nabla u\|_{L^1([0,\infty);L^\infty)}$. The key ingredients of the proof lie in the new observations for the effective viscous flux and new decay estimates for the density via the Lagrangian coordinate.
