On Energy Conservation for Stochastically Forced Fluid Flows
摘要
In this note, we discuss energy balance laws for stochastically forced fluid flows. We establish energy-balance laws for pathwise weak solutions of the stochastically forced incompressible Euler equations, having certain Besov regularity. As an application, we obtain energy balance laws for the stochastic inhomogeneous incompressible Euler system and stochastic incompressible Navier-Stokes equation. Additionally, we show the energy balance laws for compressible Euler equation and Navier-Stokes equation when density have possible vacuum region.