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arXiv · 1908.11695

Semiflow selection for the compressible Navier-Stokes system

Danica Basarić
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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.

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Danica Basarić. 2019-08-29. Semiflow selection for the compressible Navier-Stokes system. https://doi.org/10.1007/s00028-020-00578-x

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