Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations
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Publication:3638931
DOI10.1017/S0962492906420018zbMath1422.76041OpenAlexW2115331483MaRDI QIDQ3638931
Publication date: 28 October 2009
Published in: Acta Numerica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0962492906420018
Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Blow-up in context of PDEs (35B44) Euler equations (35Q31)
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Cites Work
- Unnamed Item
- On the partial regularity of a 3D model of the Navier-Stokes equations
- On the interior regularity of weak solutions of the Navier-Stokes equations
- Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations
- Blowup or no blowup? the interplay between theory and numerics
- Remarks on the breakdown of smooth solutions for the 3-D Euler equations
- Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations
- The evolution of a turbulent vortex
- Singularity formation for complex solutions of the 3D incompressible Euler equations
- On the stability of the unsmoothed Fourier method for hyperbolic equations
- Bilinear estimates in \(BMO\) and the Navier-Stokes equations
- On the regularity of the axisymmetric solutions of the Navier-Stokes equations
- Computing nearly singular solutions using pseudo-spectral methods
- Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics
- Global regularity for the 2D Boussinesq equations with partial viscosity terms
- Un teorema di unicita per le equazioni di Navier-Stokes
- 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity
- Collapsing solutions to the 3-D Euler equations
- Global Regularity of the 3D Axi-Symmetric Navier–Stokes Equations with Anisotropic Data
- Velocity and scaling of collapsing Euler vortices
- On the stabilizing effect of convection in three-dimensional incompressible flows
- On partial regularity results for the navier-stokes equations
- Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes
- Evidence for a singularity of the three-dimensional, incompressible Euler equations
- Geometric Statistics in Turbulence
- Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
- A simple one‐dimensional model for the three‐dimensional vorticity equation
- Partial regularity of suitable weak solutions of the navier-stokes equations
- Direct numerical simulation of transition to turbulence from a high-symmetry initial condition
- Vortex intensification and collapse of the Lissajous-elliptic ring: single- and multi-filament Biot-Savart simulations and visiometrics
- Geometric constraints on potentially
- Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions
- Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation
- Convergence Analysis of the Energy and Helicity Preserving Scheme for Axisymmetric Flows
- Dynamic stability of the three‐dimensional axisymmetric Navier‐Stokes equations with swirl
