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

2018/03/20 by Di Wu, Wu, Di
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1803.07371

arXiv admin note: text overlap with arXiv:1407.4156 by other authors

arxiv created 2018/03/20 · openalex publication_date 2018/03/20 · arxiv updated 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• Sur le mouvement d'un liquide visqueux emplissant l'espace
• Cauchy problem for the incompressible Navier-Stokes equation with an external force
• Blow-up of critical Besov norms at a potential Navier-Stokes singularity

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• The Navier-Stokes equations for Incompressible Flows: solution properties at potential blow-up times