An alternative approach to regularity for the Navier-Stokes equations in critical spaces

DOI10.1016/j.anihpc.2010.10.004zbMath1220.35119arXiv0908.3349OpenAlexW1968102647MaRDI QIDQ532447

Gabriel S. Koch, Carlos E. Kenig

Publication date: 4 May 2011

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.3349

zbMATH Keywords

Navier-Stokes equationregularity of the solution

Mathematics Subject Classification ID

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

Related Items (26)

Rigidity and trace properties of divergence-measure vector fields ⋮ Blow-up of critical Besov norms at a potential Navier-Stokes singularity ⋮ Quantitative bounds for critically bounded solutions to the Navier-Stokes equations ⋮ Blow-up criterion and examples of global solutions of forced Navier-Stokes equations ⋮ The existence, uniqueness, and regularity for an incompressible Newtonian flow with intrinsic degree of freedom ⋮ Blow-up criteria for the Navier-Stokes equations in non-endpoint critical Besov spaces ⋮ A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion ⋮ About the behavior of regular Navier-Stokes solutions near the blow up ⋮ On the stability of global solutions to the three-dimensional Navier-Stokes equations ⋮ Dynamical behavior for the solutions of the Navier-Stokes equation ⋮ Profile decomposition in Sobolev spaces and decomposition of integral functionals. I: Inhomogeneous case ⋮ The Navier-Stokes equations in nonendpoint borderline Lorentz spaces ⋮ Interior and boundary regularity for the Navier-Stokes equations in the critical Lebesgue spaces ⋮ Nonlocal Navier-Stokes problems in abstract function spaces and applications ⋮ Blow-up of a critical Sobolev norm for energy-subcritical and energy-supercritical wave equations ⋮ Scaling-invariant Serrin criterion via one velocity component for the Navier-Stokes equations ⋮ Global, decaying solutions of a focusing energy-critical heat equation in \(\mathbb{R}^4\) ⋮ Blow-up of critical norms for the 3-D Navier-Stokes equations ⋮ Hölder continuity for a drift-diffusion equation with pressure ⋮ Ill-posedness for the Navier-Stokes equations in critical Besov spaces \(\dot{B}_{\infty, q}^{- 1}\) ⋮ Global weak Besov solutions of the Navier-Stokes equations and applications ⋮ Solutions in mixed-norm Sobolev-Lorentz spaces to the initial value problem for the Navier-Stokes equations ⋮ Finite time blowup for an averaged three-dimensional Navier-Stokes equation ⋮ Blow-up of the critical Sobolev norm for nonscattering radial solutions of supercritical wave equations on $\mathbb{R}^{3}$ ⋮ Below-threshold solutions of a focusing energy-critical heat equation in ℝ⁴ ⋮ Blowup criterion for Navier-Stokes equation in critical Besov space with spatial dimensions \(d \geq 4\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liouville theorems for the Navier-Stokes equations and applications
• Concentration compactness for critical wave maps
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Global well-posedness and scattering for the mass-critical Hartree equation with radial data
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates
• On Leray's self-similar solutions of the Navier-Stokes equations
• Asymptotics and stability for global solutions to the Navier-Stokes equations.
• Unique continuation for parabolic operators
• Backward uniqueness for parabolic equations
• Non-blowup at large times and stability for global solutions to the Navier-Stokes equations
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• On the Navier-Stokes initial value problem. I
• Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions
• Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
• On the blow up phenomenon of the critical nonlinear Schrödinger equation
• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
• On the local smoothness of solutions of the Navier-Stokes equations
• Profile decomposition for solutions of the Navier-Stokes equations
• Profile decompositions for critical Lebesgue and Besov space embeddings
• Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in ℝ¹⁺ⁿ
• Modern Fourier Analysis
• Minimal-mass blowup solutions of the mass-critical NLS
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• Description of the lack of compactness for the Sobolev imbedding
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• Uniqueness of mild solutions of the Navier-Stokes equation and maximal Lp-regularity
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Partial regularity of suitable weak solutions of the navier-stokes equations
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Un théorème de persistance de la régularité en norme d'espaces de Besov pour les solutions de Koch et Tataru des équations de Navier–Stokes dans
• On the blow-up phenomenon for the mass-critical focusing Hartree equation in R⁴
• Well-posedness for the Navier-Stokes equations
• Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces
• On the defect of compactness for the Strichartz estimates of the Schrödinger equations
• Global regularity of wave maps. II: Small energy in two dimensions

This page was built for publication: An alternative approach to regularity for the Navier-Stokes equations in critical spaces