Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
arXiv:2106.12435 · doi:10.1007/s00021-022-00713-3
Abstract
We introduce dissipative solutions to the compressible Navier-Stokes system with potential temperature transport motivated by the concept of Young measures. We prove their global-in-time existence by means of convergence analysis of a mixed finite element-finite volume method. If a classical solution to the compressible Navier-Stokes system with potential temperature transport exists, we prove the strong convergence of numerical solutions. Our results hold for the full range of adiabatic indices including the physically relevant cases in which the existence of global-in-time weak solutions is open.
References in corpus (5)
- Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
- Existence of weak solutions for compressible Navier-Stokes equations with entropy transport
- Stochastic Galerkin method for cloud simulation
- Dissipative measure-valued solutions to the compressible Navier-Stokes system
- Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
Cited by in corpus (4)
- Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
- DMV-strong uniqueness principle for the compressible Navier-Stokes system with potential temperature transport
- Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport
- Global strong solutions to the compressible Navier-Stokes system with potential temperature transport