论文标题
在不均匀的滑入边界值问题上，稳定的可压缩通道流动
On an inhomogeneous slip-inflow boundary value problems for a steady viscous compressible channel flows
论文作者
论文摘要
我们证明了强溶液对稳定的等质压缩的Navier-Stokes方程的强大解决方案的存在和唯一性，具有流入边界条件的密度和混合边界条件，用于剪切流周围的速度。特别是，考虑了提交的速度的墙壁上的整个Navier边界条件，而墙上的完整Navier边界条件被考虑到边界的流入和流出部分。为了我们的结果，对摩擦系数$α$的幅度没有任何限制，而粘性系数$μ$的适当大假设就足够了。我们证明的重要成分之一是流场引起的优雅转换。在这种转换的帮助下，我们可以克服由连续性方程的双曲线造成的困难，为线性化系统建立先验估计值并应用固定点参数。
We prove the existence and uniqueness of strong solutions to the steady isentropic compressible Navier-Stokes equations with inflow boundary conditions for density and mixed boundary conditions for the velocity around a shear flow. In particular, the Dirichlet boundary condition on inflow and outflow part of the boundary while the full Navier boundary conditions on the wall $Γ_{0}$ for the velocity filed are considered. For our result, there are no restrictions on the amplitude of friction coefficients $α$, and the appropriately large hypothesis for the viscous coefficients $μ$ is enough. One of the substantial ingredients of our proof is an elegant transformation induced by the flow field. With the help of this transformation, we can overcome the difficulties caused by the hyperbolicity of continuity equation, establish the a priori estimates for a linearized system and apply the fixed point arguments.
