Maximal $L^p-L^q$ regularity to the Stokes Problem with Navier boundary conditions

TL;DR

This paper establishes maximal $L^p-L^q$ regularity results for the non-homogeneous Stokes problem with Navier boundary conditions, using complex and fractional powers of the Stokes operator involving the stress tensor.

Contribution

It introduces new analysis of the Stokes operator with Navier boundary conditions, enabling maximal regularity results for related parabolic problems.

Findings

Proves maximal $L^p-L^q$ regularity for the Stokes problem

Analyzes complex and fractional powers of the Stokes operator

Provides foundational results for parabolic Stokes problems with Navier boundary conditions

Abstract

We prove in this paper some results on the complex and fractional powers of the Stokes operator with slip frictionless boundary conditions involving the stress tensor. This is fundamental and plays an important role in the associated parabolic problem and will be used to prove maximal $L^{p}-L^{q}$ regularity results for the non-homogeneous Stokes problem.