Existence and uniqueness of maximal solutions to SPDEs with applications to viscous fluid equations

Abstract We present two criteria for the existence and uniqueness of a maximal strong solution general class stochastic partial differential equations. Each criterion has its corresponding set assumptions can be applied to viscous fluid equations with additive, multiplicative or transport type noise. In particular, we apply these demonstrate well-posedness results 3D SALT [Stochastic Advection by Lie Transport, (Holm in Proc R Soc A Math Phys Eng Sci 471:20140963, 2015)] Navier–Stokes Equation velocity vorticity form, on torus bounded domain respectively.