Blow-up criterion and examples of global solutions of forced Navier-Stokes equations

TL;DR

This paper establishes a blow-up criterion for forced Navier-Stokes solutions and provides examples of global solutions with large initial data using profile decomposition techniques.

Contribution

It introduces a new blow-up criterion for forced Navier-Stokes equations and constructs global solutions with large initial data.

Findings

Blow-up criterion for solutions with time-independent force

Existence of global solutions with large initial data

Use of profile decomposition method

Abstract

In this paper we first show a blow-up criterion for solutions to the Navier-Stokes equations with a time-independent force by using the profile decomposition method. Based on the orthogonal properties related to the profiles, we give some examples of global solutions to the Navier-Stokes equations with a time-independent force, whose initial data are large.