Blow-up of critical Besov norms at a potential Navier-Stokes singularity

DOI10.1007/s00220-016-2593-zzbMath1342.35217arXiv1407.4156OpenAlexW1524638442MaRDI QIDQ273191

Isabelle Gallagher, Fabrice Planchon, Gabriel S. Koch

Publication date: 21 April 2016

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

Full work available at URL: https://arxiv.org/abs/1407.4156

zbMATH Keywords

three-dimensional Navier-Stokes equationsBesov normsblowup criterion

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Blow-up in context of PDEs (35B44)

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Cites Work

• A certain necessary condition of potential blow up for Navier-Stokes equations
• An alternative approach to regularity for the Navier-Stokes equations in critical spaces
• Minimal initial data for potential Navier-Stokes singularities
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• The Navier-Stokes equations in nonendpoint borderline Lorentz spaces
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Asymptotic behavior of global solutions to the Navier-Stokes equations in \(\mathbb{R}^3\)
• Analysis of the lack of compactness in the critical Sobolev embeddings
• On Leray's self-similar solutions of the Navier-Stokes equations
• A generalization of a theorem by Kato on Navier-Stokes equations
• Asymptotics and stability for global solutions to the Navier-Stokes equations.
• On the stability of global solutions to Navier--Stokes equations in the space
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• A profile decomposition approach to the \(L^\infty _t(L^{3}_x)\) Navier-Stokes regularity criterion
• Convolution operators and L(p, q) spaces
• Profile decomposition for solutions of the Navier-Stokes equations
• Profile decompositions for critical Lebesgue and Besov space embeddings
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Self-improving bounds for the Navier-Stokes equations
• Well-posedness for the Navier-Stokes equations