On initial-boundary value problem of the stochastic Navier--Stokes equations in the half space

TL;DR

This paper investigates the initial-boundary value problem for stochastic Navier--Stokes equations in a half space, establishing the existence of weak solutions within critical Besov spaces for initial data.

Contribution

It provides a rigorous proof of weak solutions' existence for stochastic Navier--Stokes equations in half space with initial data in critical Besov spaces, advancing mathematical understanding.

Findings

Existence of weak solutions in Besov spaces

Solutions exist for initial data in critical Besov spaces

Mathematical framework for stochastic Navier--Stokes in half space

Abstract

We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the critical Besov space.