Doubly Connected V-States in Geophysical Models: A General Framework

In this paper, we prove the existence of doubly connected V-states (rotating patches) close to an annulus for active scalar equations with completely monotone kernels. This provides a unified framework for various results related to geophysical flows. This allows us to recover existing results on this topic while also extending to new models, such as the gSQG and QGSW equations in radial domains and 2D Euler equation in annular domains.