2018/07/13 by Jan Březina, Jan BŘEZINA, Eduard Feireisl +1 · 45 citations
Engineering · Mathematics · #Algorithm #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Computer science #Dissipation #Dissipative system #Euler equations #Euler system #Euler's formula #Fluid Dynamics and Turbulent Flows #Inviscid flow #Mathematical analysis #Mathematics #Measure (data warehouse) #Navier-Stokes equation solutions #Parameterized complexity #Physics #Thermodynamics
paper · pdf · doi:10.2969/jmsj/77337733
published in Journal of the Mathematical Society of Japan 70(4) (Mathematical Society of Japan)
openalex publication_date 2018/07/13 · crossref created 2018/07/13 · crossref issued 2018/10/01 · crossref published 2018/10/01 · crossref published-print 2018/10/01 · crossref deposited 2022/08/27 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/08/01
We introduce the concept of dissipative measure-valued solution to the complete Euler system describing the motion of an inviscid compressible fluid. These solutions are characterized by a parameterized (Young) measure and a dissipation defect in the total energy balance. The dissipation defect dominates the concentration errors in the equations satisfied by the Young measure. A dissipative measure-valued solution can be seen as the most general concept of solution to the Euler system retaining its structural stability. In particular, we show that a dissipative measure-valued solution necessarily coincides with a classical one on its life span provided they share the same initial data.