论文标题
低马赫数的统一规律性和范围内完整的Navier-Stokes系统的无关限制
Uniform regularity in the low Mach number and inviscid limits for the full Navier-Stokes system in domains with boundaries
论文作者
论文摘要
在目前的工作中，在对低马赫数限制问题的研究中，我们就具有纳维尔 - 滑行边界条件的平滑域中的非异形可压缩的Navier-Stokes系统建立了统一的规律性估计，在不准备好的初始数据的一般情况下。考虑热传导，并允许温度的较大变化。此外，在[1，+\ infty）中的reynolds $ \ text {re} \ in [1，+\ infty），$péclet编号$ \ text {pe} \ in [1，+\ infty），提供的$péclet$ \ in [1，+\ infty），$ in [1，+\ infty）''，$pécletnumber in [1，+\ infty），$ in Number number $ \ text {re} \ in [1，+\ infty），$ in [1，+\ infty）''，提供的规律性估计值也均匀。 $$ \ big | \ frac {1} {\ text {re}} - \ frac {i_0} {\ text {pe}} \ big | \ big | \ sillsim \ frac {1} {\ text {pe}^{\ frac {1} {2}}}} \ frac {1} {1} {\ text {re}}，$ $，其中$ i_0 $是固定的常数，固定常数是独立于马赫数，reynolds编号，和péclet编号。较大的温度变化以及两种边界层的相互作用是证明的主要障碍。
In the present work, motivated by the studies on the low Mach number limit problem, we establish uniform regularity estimates with respect to the Mach number for the non-isentropic compressible Navier-Stokes system in smooth domains with Navier-slip boundary conditions, in the general case of ill-prepared initial data. The thermal conduction is taken into account and the large variation of temperature is allowed. Moreover, the obtained regularity estimates are also uniform in the Reynolds number $\text{Re}\in[1,+\infty),$ Péclet number $\text{Pe}\in [1,+\infty),$ provided $$\big|\frac{1}{\text{Re}}-\frac{ι_0}{\text{Pe}}\big|\lesssim \frac{1}{\text{Pe}^{\frac{1}{2}}}\frac{1}{\text{Re}},$$ where $ι_0$ is a fixed constant independent of the Mach number, Reynolds number, and Péclet number. The large temperature variation as well as the interactions of two kinds of boundary layers are the main obstacles to the proof.
