DMV-strong uniqueness principle for the compressible Navier-Stokes system with potential temperature transport
This result provides theoretical stability for strong solutions in a generalized solution framework, relevant for mathematicians studying fluid dynamics and PDEs.
The paper proves that strong solutions of the compressible Navier-Stokes system with potential temperature transport are unique within the class of dissipative measure-valued solutions, establishing a DMV-strong uniqueness principle.
We establish a DMV-strong uniqueness result for the compressible Navier-Stokes system with potential temperature transport. The concept of generalized, the so-called dissipative measure-valued (DMV), solutions was proposed in [7], where their global-in-time existence was proved. Here we show that strong solutions are stable in the class of DMV solutions. More precisely, a DMV solution coincides with a strong solution emanating from the same initial data as long as the strong solution exists.