3D Euler equations and ideal MHD mapped to regular systems: Probing the finite-time blowup hypothesis (original) (raw)

On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations

Thomas Hou

arXiv (Cornell University), 2013

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On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations

Thomas Hou

Archive for Rational Mechanics and Analysis, 2014

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Singular solutions to the 3D axisymmetric incompressible Euler equations

Alain Pumir

Physica D: Nonlinear Phenomena, 1992

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An unfinished tale of nonlinear PDEs: Do solutions of 3D incompressible Euler equations blow-up in finite time?

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Physica D: Nonlinear Phenomena, 2005

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Finite-time singularities in the axisymmetric three-dimension Euler equations

Alain Pumir

Physical Review Letters, 1992

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Improved Geometric Conditions for Non-Blowup of the 3D Incompressible Euler Equation

Thomas Hou

Communications in Partial Differential Equations, 2006

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Note on loss of regularity for solutions of the 3?D incompressible euler and related equations

Popescu Constantin

Communications in Mathematical Physics, 1986

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A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

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Theoretical and Computational Fluid Dynamics, 2017

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Non blow-up of the 3D Euler equations for a class of three-dimensional initial data in cylindrical domains

Alex Mahalov

Methods and Applications of Analysis, 2004

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Potential Singularity of the 3D Euler Equations in the Interior Domain

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Foundations of Computational Mathematics

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On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations

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Communications on Pure and Applied Mathematics

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The three-dimensional Euler equations: singular or non-singular?

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Nonlinearity, 2008

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Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations

Thomas Hou

Acta Numerica, 2009

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Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation

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A Hamiltonian Description of Finite-Time Singularity in Euler's Fluid Equations

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Non-blow-up of the 3D ideal magnetohydrodynamics equations for a class of three-dimensional initial data in cylindrical domains

Alex Mahalov

Journal of Mathematical Sciences, 2006

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The 3D incompressible Euler equations with a passive scalar : a road to blow-up?

J D Gibbon

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Title The 3 D incompressible euler equations with a passive scalar : A road to blow-up ?

Edriss Titi

2013

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Ju l 2 01 5 A Blow-Up Criterion for the 3 D Euler Equations Via the Euler-Voigt Inviscid Regularization

Edriss Titi

2015

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Potentially singular solutions of the 3D axisymmetric Euler equations

Thomas Hou

Proceedings of the National Academy of Sciences of the United States of America, 2014

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OPEN PROBLEM The three-dimensional Euler equations: singular or non-singular

J D Gibbon

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On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models

Edriss Titi

Discrete and Continuous Dynamical Systems - Series B, 2010

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On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

Thomas Hou

2014

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A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization

Edriss Titi

arXiv: Analysis of PDEs, 2015

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Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations

J D Gibbon

Physical review. E, 2016

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On singularity formation of a 3 D model for incompressible Navier – Stokes equations

Thomas Hou

2010

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Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations (Nonlinearity

J D Gibbon

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Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations

Manwai Yuen

Physics Letters A, 2011

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Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations

Thomas Hou

Journal of Nonlinear Science, 2006

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Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations

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Mathematics and Computation, a Contemporary View, 2008

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Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: A Numerics Guided Study

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SIAM Review

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Exact, infinite energy, blow-up solutions of the three-dimensional Euler equations

J D Gibbon

Nonlinearity, 2003

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