Dissipative solutions and semiflow selection for the complete Euler system
arXiv:1904.00622 · doi:10.1007/s00220-019-03662-7
Abstract
To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at selection of physically relevant solutions. Even under the presence of infinitely many solutions to the full Euler system describing the motion of a compressible inviscid fluid, our approach permits to select a system of solutions (one trajectory for every initial condition) satisfying the classical semiflow property. Moreover, the selection respects the well accepted admissibility criteria for physical solutions, namely, maximization of the entropy production rate and the weak--strong uniqueness principle. Consequently, strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well. To this end, we introduce a notion of dissipative solution, which is given by a triple of density, momentum and total entropy defined as expectations of a suitable measure--valued solution.
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Cited by in corpus (9)
- Maximal dissipative solutions for incompressible fluid dynamics
- Statistical solutions to the barotropic Navier-Stokes system
- Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
- Ergodic theory for energetically open compressible fluid flows
- Semiflow selection for the compressible Navier-Stokes system
- Probabilistic Descriptions of Fluid Flow: A Survey
- Non-Uniqueness in Plane Fluid Flows
- Semiflow selection to models of general compressible viscous fluids
- Limit of a consistent approximation to the complete compressible Euler System