Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions

2024/01/30 by Xiangsheng Xu, Xu, Xiangsheng
Mathematics · Physics and Astronomy · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Cosmology and Gravitation Theories

paper · pdf · doi:10.48550/arxiv.2401.17147

Abstract

We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one whenever the initial velocity is divergence free and uniformly bounded with finite energy. Our results seem to have given a positive answer to the Navier-Stokes millennium problem proposed by the Clay Mathematical Institute.

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

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