Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces

DOI10.1063/1.4765332zbMath1426.76089arXiv1212.4207OpenAlexW3099342367MaRDI QIDQ2872375

Alexey Cheskidov, Roman Shvydkoy

Publication date: 14 January 2014

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

Full work available at URL: https://arxiv.org/abs/1212.4207

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (6)

Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in \(\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}\) ⋮ Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces ⋮ Sobolev multipliers, maximal functions and parabolic equations with a quadratic nonlinearity ⋮ Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces ⋮ Algebra properties in Fourier-Besov spaces and their applications ⋮ Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type

Cites Work

• The regularity of weak solutions of the 3D Navier-Stokes equations in \(B^{-1}_{\infty,\infty}\)
• Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Un teorema di unicita per le equazioni di Navier-Stokes
• Well-posedness for fractional Navier-Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn)
• Classical Fourier Analysis
• Ill-posedness of the basic equations of fluid dynamics in Besov spaces
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Finite time blow-up for a dyadic model of the Euler equations
• Well-posedness for the Navier-Stokes equations
• Unnamed Item

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