On the local Smoothness of Solutions of the Navier-Stokes Equations

2005/02/05 by Hongjie Dong, Dong, Hongjie, Dapeng Du +1 · 1 citation
Engineering · Mathematics · #35Q30 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35Q30 #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.math/0502104

14 pages

arxiv created 2005/02/05 · openalex publication_date 2005/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for incompressible Navier-Stokes equations u_t+u∇_xu-Δu+∇ p=0, div u=0 in R^d × R⁺ with initial data a∈ L^d(R^d), and study in some detail the smoothing effect of the equation. We prove that for T

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

Cited by

• Regularity of solutions to the Navier-Stokes equations evolving from\n small data in BMO^-1

Related

• Well-posedness, Smoothness and Blow-up for Incompressible Navier-Stokes Equations
• Smooth Solutions of the Navier-Stokes Equation in L_p(R³)
• Weak Solutions for the Navier-Stokes Equations for B^-1(ln)_∞∞+B_X_r^{-1+r,(2)/(1-r)}+L² Initial Data
• Global in time solution to the incompressible Navier-Stokes equations on \Realⁿ. An Elementary Approach
• Global Regularity to the Navier-Stokes Equations for A Class of Large Initial Data