Ill-posedness of the basic equations of fluid dynamics in Besov spaces

DOI10.1090/S0002-9939-09-10141-7zbMath1423.76085arXiv0904.2196MaRDI QIDQ3550579

Alexey Cheskidov, Roman Shvydkoy

Publication date: 31 March 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.2196

zbMATH Keywords

Euler equationBesov spacesNavier-Stokes equationill-posedness

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Euler equations (35Q31)

Related Items (26)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The regularity of weak solutions of the 3D Navier-Stokes equations in \(B^{-1}_{\infty,\infty}\)
• On the energy of inviscid singular flows
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Hydrodynamics in Besov spaces
• On the strong solvability of the Navier-Stokes equations
• Vorticity and Incompressible Flow
• Existence of Solution for the Euler Equations in a Critical Besov Space (ℝⁿ)
• Energy conservation and Onsager's conjecture for the Euler equations
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires

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