Galerkin approximation and the strong solution of the Navier-Stokes equation (Q1841231)

The existence of strong solutions using Galerkin-type approximations associated with stochastic Navier-Stokes equations is studied. The diffusion part is linearly depending on the unknown function and the Galerkin-type approximations convergence in mean square to the strong solution. There are used properties of stopping times and some basic convergence principles from functional analysis. It is recommended to those working with stochastic partial differential equations.