论文标题
1D可压缩的Navier-Stokes系统的全球适合性，并具有粗略的数据
Global well-posedness of the 1d compressible Navier-Stokes system with rough data
论文作者
论文摘要
在本文中，我们研究了具有粗略的初始数据的气体动力学中1D可压缩纳维尔 - 蒸汽系统（CNSE）的全球适应性问题。弗里斯特（Liu- Yu）（2022）为1D等性CNSE建立了全球适应性理论，并在BV空间中具有初始速度数据。然后，将其扩展到1D CNSE，以通过Wang-Yu-Zhang（2022）在BV空间中具有初始速度和温度数据的多粒子理想气体。我们在$ w^{2γ，1} $ space中使用初始速度数据改善了刘Yu的全球良好性结果；及Wang-Yu-Zhang的初始速度数据中的$ l^2 \ cap w^{2γ，1} $ space和$ \ dot w^{ - \ frac {2} {2} {3} {3}，\ frac {6} {6} {5} {5}} {5}} {5}} {5}} \ cap \ cap \ cap \ cap \ cap \ cap \ cap \ cap \ cop \ cap \ cop \ dot w^^2γ-1 \ textit {任意小}。我们的基本思想是基于为一维抛物线方程式建立各种“终点”平滑估计。
In this paper, we study the global well-posedness problem for the 1d compressible Navier-Stokers system (cNSE) in gas dynamics with rough initial data. Frist, Liu- Yu (2022) established the global well-posedness theory for the 1d isentropic cNSE with initial velocity data in BV space. Then, it was extended to the 1d cNSE for the polytropic ideal gas with initial velocity and temperature data in BV space by Wang-Yu-Zhang (2022). We improve the global well-posedness result of Liu-Yu with initial velocity data in $W^{2γ,1}$ space; and of Wang-Yu-Zhang with initial velocity data in $ L^2\cap W^{2γ,1}$ space and initial data of temperature in $\dot W^{-\frac{2}{3},\frac{6}{5}}\cap \dot W^{2γ-1,1}$ for any $γ>0$ \textit{arbitrary small}. Our essential ideas are based on establishing various "end-point" smoothing estimates for the 1d parabolic equation.
