Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations

DOI10.1090/S0002-9939-09-09765-2zbMath1162.76016arXiv0805.3215OpenAlexW1978313382MaRDI QIDQ3629431

Marius Paicu, Isabelle Gallagher

Publication date: 27 May 2009

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

Full work available at URL: https://arxiv.org/abs/0805.3215

zbMATH Keywords

global solutiondivergence-free condition

Mathematics Subject Classification ID

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

Related Items (14)

On a toy-model related to the Navier-Stokes equations ⋮ Global regularity for a model of Navier-Stokes equations with logarithmic sub-dissipation ⋮ Global regularity for a 3D Boussinesq model without thermal diffusion ⋮ Blow‐up regions for a class of fractional evolution equations with smoothed quadratic nonlinearities ⋮ Finite-time blowup for a Navier-Stokes model equation for the self-amplification of strain ⋮ Near-invariance under dynamic scaling for Navier–Stokes equations in critical spaces: a probabilistic approach to regularity problems ⋮ On the global solvability of the axisymmetric Boussinesq system with critical regularity ⋮ Global regularity for some classes of large solutions to the Navier-Stokes equations ⋮ A bounded numerical solution with a small mesh size implies existence of a smooth solution to the Navier-Stokes equations ⋮ An analogue scalar model for the Navier Stokes equations ⋮ Finite time blowup for an averaged three-dimensional Navier-Stokes equation ⋮ Blow-up results to certain hyperbolic model problems in fluid mechanics ⋮ Towards spaces of harmonic functions with traces in square Campanato spaces and their scaling invariants ⋮ A new path to the non blow-up of incompressible flows

Cites Work

• On global infinite energy solutions to the Navier-Stokes equations in two dimensions
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• On the Navier-Stokes initial value problem. I
• Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method
• Navier-Stokes equations in \(\mathbb R^2\): existence and asymptotic behavior of infinite energy solutions
• Finite time blow up for a Navier-Stokes like equation
• Three-dimensional blow-up solutions of the Navier-Stokes equations
• Well-posedness for the Navier-Stokes equations
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