可压缩流体Navier-Slip边界条件问题解的存在性研究

Local Solutions of a Compressible Flow Problem with Navier-Slip Boundary Conditions

证明了在有界区域Ω■R^3中带Navier-Slip边界条件的可压缩Navier-Stokes方程的解的局部存在性.在证明过程中,首先利用线性化方法将方程转化为线性方程,再利用Galerkin逼近方法得到线性方程组的弱解,通过能量估计方法,得到关于逼近解的一致先验估计,取极限得到方程的解的局部存在性.

The study shows that there exist local-in-time solutions of the compressible Navier-Stoke equations with Navier-Slip boundary conditions in a bounded domain Ω∈R^3.To this end,the linearization approach,Galerkin method,aprior estimates and uniform convergence theorem have been used.