On the Use of the Riesz Transforms to Determine the Pressure Term in the Incompressible Navier-Stokes Equations on the Whole Space

Abstract:

We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire d-dimensional Euclidean space is determined by the formula ∇p=∇(∑i,j=1dRiRj(uiuj−Fi,j)), where d∈ { 2 , 3 } , u: = (u1, … , ud) is the fluid velocity, F:=(Fi,j)1≤i,j≤d is the forcing tensor, and for all k∈ { 1 , … , d} , Rk is the k-th Riesz transform.

Año de publicación:

2021

Keywords:

• Pressure term
• Navier-Stokes equations
• Weighted spaces
• Riesz transforms

Fuente:

scopus