This talk discusses various applications of the relative entropy method in the context of fluid mechanics, focusing on weak-strong uniqueness results and asymptotic limits. Particular attention is given to Euler-type equations involving nonlocal interactions. Furthermore, I will present recent results regarding a novel approach to pressureless Euler equations.
Another application of the relative entropy method to be discussed is the unconditional stability of certain radially symmetric steady states for compressible viscous fluids in domains with inflow/outflow boundary conditions. Specifically, we demonstrate that any solution to the associated evolutionary problem, not necessarily radially symmetric, converges to a unique radially symmetric steady state.