Partial regularity of solutions to the four-dimensional Navier-Stokes equations at the first blow-up time

DOI10.1007/s00220-007-0259-6zbMath1156.35442arXivmath/0601113OpenAlexW3103839689MaRDI QIDQ946512

Hongjie Dong, Dapeng Du

Publication date: 23 September 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0601113

zbMATH Keywords

Navier-Stokes equationsHausdorff measureregularity of solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (21)

Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6 ⋮ Partial regularity of solutions to the fractional Navier-Stokes equations ⋮ Sharp nonuniqueness for the Navier-Stokes equations ⋮ Partially regular weak solutions of the Navier-Stokes equations in \(\mathbb{R}^4 \times [0,\infty[\) ⋮ Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations ⋮ Local \(\varepsilon\)-regularity criteria for the five dimensional stationary Navier-Stokes equations ⋮ Interior and boundary regularity for the Navier-Stokes equations in the critical Lebesgue spaces ⋮ Large time behavior for the nonstationary Navier-Stokes flows in the half-space ⋮ Long-time behavior for Navier-Stokes flows in a two-dimensional exterior domain ⋮ A unified proof on the partial regularity for suitable weak solutions of non-stationary and stationary Navier-Stokes equations ⋮ Boundary partial regularity for the high dimensional Navier-Stokes equations ⋮ On the Navier-Stokes equations in scaling-invariant spaces in any dimension ⋮ Regularity conditions for suitable weak solutions of the Navier-Stokes system from its rotation form ⋮ The Navier-Stokes equations in the critical Lebesgue space ⋮ Decay results of higher-order norms for the Navier-Stokes flows in 3D exterior domains ⋮ Partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow ⋮ On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations ⋮ Blowup criterion for Navier-Stokes equation in critical Besov space with spatial dimensions \(d \geq 4\) ⋮ Numerical study on comparison of Navier-Stokes and Burgers equations ⋮ Interior and boundary regularity criteria for the 6D steady Navier-Stokes equations ⋮ Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Solutions in \(L_ r\) of the Navier-Stokes initial value problem
• The Navier-Stokes equations on a bounded domain
• Partial regularity of solutions to the Navier-Stokes equations
• Hausdorff measure and the Navier-Stokes equations
• The Navier-Stokes equations in space dimension four
• The resolution of the Navier-Stokes equations in anisotropic spaces
• A generalization of a theorem by Kato on Navier-Stokes equations
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations
• Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations
• Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Navier-stokes flow in r³with measures as initial vorticity and morrey spaces
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Well-posedness for the Navier-Stokes equations

This page was built for publication: Partial regularity of solutions to the four-dimensional Navier-Stokes equations at the first blow-up time