So far existence of dissipative weak solutions for the compressible Navier–Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e., in particular, when the normal component of the velocity on the boundary of the flow domain is equal to zero). Most of physical applications (as flows in wind tunnels, pipes, reactors of jet engines) requires to consider non-zero inflow–outflow boundary condtions. We prove existence of dissipative weak solutions to the compressible Navier–Stokes equations in barotropic regime (adiabatic coefficient \(\gamma >3/2\), in three dimensions, \(\gamma >1\) in two dimensions) with large velocity prescribed at the boundary and large density prescribed at the inflow boundary of a bounded piecewise regular Lipschitz domain, without any restriction neither on the shape of the inflow/outflow boundaries nor on the shape of the domain. It is well known that the relative energy inequality has many applications, e.g., to investigation of incompressible or inviscid limits, to the dimension reduction of flows, to the error estimates of numerical schemes. In this paper we deal with one of its basic applications, namely weak–strong uniqueness principle.

到目前为止，仅在边界条件为非零流入/流出的情况下（即，当正态分量为零时）才知道可压缩Navier-Stokes方程的耗散弱解（即满足相对能量不等式的弱解）的存在。流域边界上的速度等于零）。大多数物理应用（如风洞，管道，喷气发动机的反应堆中的流量）都需要考虑非零流入-流出边界条件。我们证明了在正压状态下（绝热系数\（\ gamma> 3/2 \）在三个维度上，\（\ gamma> 1 \）的可压缩Navier–Stokes方程存在耗散弱解。在二维中），在有界分段规则Lipschitz域的边界处规定的大速度和在流入边界处规定的大密度，既不限制流入/流出边界的形状也不限制域的形状。众所周知，相对能量不等式具有许多应用，例如，用于研究不可压缩或无粘性极限，流的尺寸减小，数值方案的误差估计。在本文中，我们处理其基本应用之一，即弱强唯一性原理。