Minimal initial data for potential Navier-Stokes singularities
Analysis of PDEs
2009-11-04 v1
Abstract
Assuming some \dot H^{1/2} - initial data lead to a singularity for the 3d Navier-Stokes equations, we show that there are also initial data with the minimal \dot H^{1/2} - norm which will produce a singularity.
Cite
@article{arxiv.0911.0500,
title = {Minimal initial data for potential Navier-Stokes singularities},
author = {Walter Rusin and Vladimir Sverak},
journal= {arXiv preprint arXiv:0911.0500},
year = {2009}
}
Comments
16 pages
Related papers
View all related →
Analysis of PDEs · Mathematics
Minimal $L^3$-initial data for potential Navier-Stokes singularities
Hao Jia, Vladimír Šverák
2012-11-12
Probability · Mathematics
The Navier-Stokes equations with transport noise in critical $H^{1/2}$ space
Mustafa Sencer Aydın, Fanhui Xu
2025-11-07
Analysis of PDEs · Mathematics
The Probabilistic Method and large initial data for Generalized Navier-Stokes systems
Jean C. Cortissoz
2011-09-12
Fluid Dynamics · Physics
The potentially singular behavior of the 3D Navier-Stokes equations
Thomas Y. Hou
2022-05-30
Analysis of PDEs · Mathematics
Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations
Juan Vicente Gutiérrez-Santacreu
2017-07-25
Analysis of PDEs · Mathematics
Initial-Boundary value problem of the Navier-Stokes equations in the half space with nonhomogeneous data
Tongkeun Chang, Bum Ja Jin
2018-06-08
Analysis of PDEs · Mathematics
Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
Jean-Yves Chemin, Isabelle Gallagher
2007-10-31
Analysis of PDEs · Mathematics
Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations
Percy Wong
2013-10-29
Analysis of PDEs · Mathematics
Almost sure existence of Navier-Stokes Equations with randomized data in the whole space
Robin Ming Chen, Dehua Wang, Song Yao, Cheng Yu
2013-10-29
Probability · Mathematics
Almost global existence for the stochastic Navier-Stokes equations with small $H^{1/2}$ data
Mustafa Sencer Aydın, Igor Kukavica, Fanhui Xu
2025-01-20
Probability · Mathematics
The stochastic Navier-Stokes equations with general $L^{3}$ data
Mustafa Sencer Aydın, Igor Kukavica, Fanhui Xu
2025-04-09
Analysis of PDEs · Mathematics
An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
2022-03-09
Analysis of PDEs · Mathematics
Global regularity for solutions of the three dimensional Navier-Stokes equation with almost two dimensional initial data
Evan Miller
2020-09-07
Analysis of PDEs · Mathematics
Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane
P. Maremonti, S. Shimizu
2018-08-29
Analysis of PDEs · Mathematics
The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution
Chao Wang, Jingchao Yue, Zhifei Zhang
2026-04-08
Analysis of PDEs · Mathematics
Almost sure existence of global weak solutions for super-critical Navier-Stokes equations
Andrea R. Nahmod, Nataša Pavlović, Gigliola Staffilani
2013-02-27
Analysis of PDEs · Mathematics
Forward self-similar solutions to the 2D Navier--Stokes equations
Dallas Albritton, Julien Guillod, Mikhail Korobkov, Xiao Ren
2026-01-07
Analysis of PDEs · Mathematics
Minimal blow-up initial data in critical Fourier-Herz spaces for potential Navier-Stokes singularities
Jingyue Li, Changxing Miao, Xiaoxin Zheng
2018-04-27
Analysis of PDEs · Mathematics
Uniqueness of solutions to to Navier Stokes equation with small initial data in $L^{3,\infty}(R^3)$
Hao Jia
2014-10-01
Analysis of PDEs · Mathematics
Wellposedness and stability results for the Navier-Stokes equations in ${\mathbf R}^{3}$
Jean-Yves Chemin, Isabelle Gallagher
2007-05-23
Analysis of PDEs · Mathematics
Global Well-Posedness for the 3D Navier-Stokes Equations under Logarithmically Improved Criteria: Connections to Turbulence Theory
Rishabh Mishra
2025-03-27
Analysis of PDEs · Mathematics
Navier-Stokes equations in the half space with non compatible data
Andrea Argenziano, Marco Cannone, Marco Sammartino
2022-02-22
Analysis of PDEs · Mathematics
Short time regularity of Navier-Stokes flows with locally $L^3$ initial data and applications
Kyungkeun Kang, Hideyuki Miura, Tai-Peng Tsai
2018-12-31
Analysis of PDEs · Mathematics
Existence of local suitable weak solutions to the Navier-Stokes equations for initial data in $L^{2}_{\rm loc} (\mathbb{R}^3)$
Dongho Chae, Joerg Wof
2022-06-29
Analysis of PDEs · Mathematics
Solvability of the Initial-Boundary value problem of the Navier-Stokes equations with rough data
Tongkeun Chang, Bum Ja Jin
2015-03-31