Lower Bounds on Blowing-Up Solutions of the Three-Dimensional Navier--Stokes Equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$

DOI10.1137/15M1017776zbMath1344.35081arXiv1503.04323OpenAlexW2436744075MaRDI QIDQ2814475

James C. Robinson, David S. McCormick, Jose L. Rodrigo, Yi Zhou, Alejandro Vidal-López, Eric J. Olson

Publication date: 22 June 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.04323

zbMATH Keywords

Sobolev spacesNavier-Stokes equationsBesov spacesblowupcommutator estimates

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Navier-Stokes equations (35Q30) Blow-up in context of PDEs (35B44)

Related Items (4)

On the blow-up criterion of magnetohydrodynamics equations in homogeneous Sobolev spaces ⋮ Navier–Stokes Blowup Rates in Certain Besov Spaces Whose Regularity Exceeds the Critical Value by \({\boldsymbol{\epsilon \in [1,2}}\)] ⋮ Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes ⋮ Lower bounds for possible singular solutions for the Navier-Stokes and Euler equations revisited

Cites Work

• Unnamed Item
• Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO
• A local smoothness criterion for solutions of the 3D Navier-Stokes equations
• On the blow-up criterion of 3D Navier-Stokes equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
• Lower bounds of potential blow-up solutions of the three-dimensional Navier-Stokes equations in Ḣ32
• Lower bounds on blow up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces
• Fourier Analysis and Nonlinear Partial Differential Equations
• Commutator estimates and the euler and navier-stokes equations
• Remarques sur l’Existence Globale Pour le Système de Navier–Stokes Incompressible
• On the blow‐up criterion of the periodic incompressible fluids
• On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation

This page was built for publication: Lower Bounds on Blowing-Up Solutions of the Three-Dimensional Navier--Stokes Equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$