Anelastic approximation for the degenerate compressible Navier-Stokes equations revisited 

I will talk about our recent result in which we revisit the low Mach and low Froude numbers limit for the compressible Navier-Stokes equations with degenerate density-dependent viscosity. Using the relative entropy inequality based on the concept of k-entropy, we rigorously justified the convergence to the generalized anelastic approximation in the three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we also obtained similar convergence result in the whole space, relying on dispersive estimates for acoustic waves.
Compared with our earlier work [Fanelli and Zatorska, Commun. Math. Phys., 2023], the present analysis removes the need for the cold pressure component, so that the pressure law is purely isentropic without any additional regularizing term. This is joint work with Nilasis Chaudhuri, Francesco Fanelli, and Yang Li.