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Main Author: Xu, Xiangsheng
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.17147
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author Xu, Xiangsheng
author_facet Xu, Xiangsheng
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_17147
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions
Xu, Xiangsheng
Analysis of PDEs
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.
title Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions
topic Analysis of PDEs
url https://arxiv.org/abs/2401.17147