On dissipative turbulent solutions to the compressible anisotropic Navier–Stokes equations in unbounded domains

Abstract We prove the global existence of dissipative turbulent solution for the compressible Navier–Stokes equations with anisotropic viscous stress tensor on unbounded domain. These solutions, introduced for compressible systems by Abbatiello, Feireisl and Novotný (2021 Discrete Contin. Dyn. Syst . 1–28), are such that they satisfy the momentum equation with a measure-valued defect which is controlled by an energy defect appearing in the energy inequality. Our work complements earlier result of Bresch and Jabin (2018 Ann. of Math . 577–684), who used the new compactness method to prove the existence of a weak solution to the same system in T 3 . By virtue of the concept of dissipative turbulent solutions, we are able to relax assumptions on the anisotropic tensor coefficients and the pressure law coefficient. We point out that we establish the existence result on a large class of unbounded domains, which is more conform to geophysical context. We also prove the weak-strong uniqueness property of acquired dissipative turbulent solutions.