Semiflow selection for the compressible Navier-Stokes system

Abstract

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.

typos corrected, Sections 3 and 4.1 rearranged, reference added, results unchanged. arXiv admin note: text overlap with arXiv:1901.04798 by other authors