The role of the Besov space \({\mathbf B}_{\infty}^{-1,\infty}\) in the control of the eventual explosion in finite time of the regular solutions of the Navier-Stokes equations

DOI10.1016/S1631-073X(03)00155-9zbMath1038.35058arXiv0906.0733OpenAlexW1551583672MaRDI QIDQ1408206

Ramzi May

Publication date: 15 September 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.0733

zbMATH Keywords

Navier-Stokes equationsmaximal solution

Mathematics Subject Classification ID

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)

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Cites Work

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• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• On the singular set and the uniqueness of weak solutions of the Navier- Stokes equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Regularity criterion of weak solutions to the Navier-Stokes equations
• Sur l'unicité dans L3ℝ3 des solutions « mild » des équations de Navier-Stokes

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