Homothetic variant of fractional Sobolev space with application to Navier-Stokes system revisited

TL;DR

This paper revisits and deepens the understanding of fractional Sobolev spaces, specifically their homothetic variants, and explores their applications to the Navier-Stokes system, building on previous work from 2007.

Contribution

It offers a refined analysis of homothetic fractional Sobolev spaces and their relevance to fluid dynamics equations like Navier-Stokes.

Findings

Enhanced theoretical framework for fractional Sobolev spaces

Improved understanding of Navier-Stokes applications

Clarification of previous results from 2007

Abstract

This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.