Inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations

TL;DR

This paper investigates the inviscid limit of the 3D Boussinesq equations with slip boundary conditions, analyzing the influence of initial data and providing insights applicable to related fluid dynamics models.

Contribution

It offers new analysis of the inviscid limit for the 3D Boussinesq equations with slip boundaries, emphasizing initial data effects and extending understanding of the vanishing viscosity limit.

Findings

Clarifies the role of initial data in the inviscid limit

Provides mathematical insights into slip boundary conditions

Connects results to applications in 3D Boussinesq equations

Abstract

In this note we consider the inviscid limit for the 3D Boussinesq equations without diffusion, under slip boundary conditions of Navier's type. We first study more closely the Navier-Stokes equations, to better understand the problem. The role of the initial data is also emphasized in connection with the vanishing viscosity limit.