论文标题
真空自由边界问题的低马赫和低弗洛德数量限制1-D可压缩纳维尔 - stokes方程的经典解决方案
Low Mach and low Froude number limit for vacuum free boundary problem of all-time classical solutions of 1-D compressible Navier-Stokes equations
论文作者
论文摘要
在本文中，我们研究了一维压缩的Navier-Stokes方程的流体 - 空白不含边界问题的历史经典解决方案的低马赫和Froude数量限制。假设存在历史解决方案的初始数据并不小。始终建立了有关马赫数和弗洛德数的溶液均匀估计值，特别是对于压力的高阶导数，这与先前的结果相反。讨论了“准备不足”的初始数据和“准备充分”的初始数据的情况。有趣的是，要么马赫数和弗洛德号都消失，要么是到无穷大的时间，限制函数是相同的，即稳态。主要困难是，该系统是在自由边界附近退化的，并包含奇异的术语。可以将此结果视为自由边界问题的低马赫和Froude数字限制的第一个结果。同时，我们还建立了经典解决方案的历史存在，其稳定速率急剧，而先前的结果仅与弱或强溶液有关。
In this paper, we study the low Mach and Froude number limit for the all-time classical solution of a fluid-vacuum free boundary problem of one-dimensional compressible Navier-Stokes equations. No smallness of initial data for the existence of all-time solutions are supposed. The uniform estimates of solutions with respect to the Mach number and the Froude number are established for all the time, in particular for high order derivatives of the pressure, which is a novelty in contrast to previous results. The cases of "ill-prepared" initial data and "well-prepared" initial data are both discussed. It is interesting to see, either both the Mach number and the Froude number vanish, or the time goes to infinity, the limiting functions are the same, that is, the steady state. The main difficulty is that, the system is degenerate near the free boundary and contains singular terms. This result can be viewed as the first one on the low Mach and Froude numbers limit for free boundary problems. At the same time, we also establish the all-time existence of the classical solution with sharp convergent rates to the steady state, while previous results are only concerned with the weak or strong solutions.
