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

  title={Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: A Numerical Investigation},
  author={Guo Luo and Thomas Y. Hou},
  journal={Multiscale Modeling & Simulation},
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries. The solutions satisfy a periodic boundary condition along the axial direction… CONTINUE READING
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