Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

Due to the intrinsic link with (kinetic) nonlinear Fokker–Planck equations and many diverse applications, distribution dependent stochastic differential have been investigated intensively in recent years. The appearance of probability distributions (or laws) random variables solutions coefficients is a distinct feature equations. In this paper, under certain averaging conditions, we establish p...