Although the existence of dissipative weak solutions for the compressible Navier–Stokes system has already been established for any finite energy initial data, uniqueness is still an open problem. The idea is then to select a solution satisfying the semigroup property, an important feature of systems with uniqueness. More precisely, we are going to prove the existence of a semiflow selection in terms of the three state variables: the density, the momentum, and the energy. Finally, we will show that it is possible to introduce a new selection defined only in terms of the initial density and momentum; however, the price to pay is that the semigroup property will hold almost everywhere in time.

尽管已经为任何有限的能量初始数据建立了可压缩的Navier-Stokes系统的耗散弱解，但是唯一性仍然是一个未解决的问题。然后的想法是选择一个满足半群性质的解决方案，这是具有唯一性的系统的重要特征。更准确地说，我们将根据三个状态变量（密度，动量和能量）证明半流选择的存在。最后，我们将表明有可能引入仅根据初始密度和动量定义的新选择。然而，要付出的代价是准集团财产将在几乎所有时间都持有。