Abstract

In this chapter, we introduce fundamental tools for studying stochastic Navier-Stokes equations with additive noise. Firstly, we present the deterministic system and explain the meaning and properties of the different terms in the equations. Then, we prove the well-posedness of the stochastic Navier-Stokes equations with additive noise using deterministic tools. The objective of this chapter is not only pedagogical, aimed at gradually familiarizing researchers with a deterministic background with the issues related to stochastic partial differential equations (SPDE), but also to present a methodology that is not optimal for studying the well-posedness of SPDEs with additive noise, but still useful for addressing other related issues.

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