Regularity and Energy Laws in Hydrodynamic Models of Newtonian Fluids and Collective Behavior

We consider several hydrodynamic models of Newtonian fluids and collective behavior, including the Euler and Navier-Stokes equations (both homogeneous and inhomogeneous) as well as the fractional Euler Alignment model. In each case we provide sufficient conditions to guarantee energy equality. We also give well-posedness results in large function spaces for the fractional Euler Alignment model, for which the existing well-posedness theory is less developed than for the other models we study.