Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with $$C^{1,\alpha }$$ Velocity and Boundary

@article{Chen2021FiniteTB,
  title={Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with \$\$C^\{1,\alpha \}\$\$ Velocity and Boundary},
  author={Jiajie Chen and Thomas Y. Hou},
  journal={Communications in Mathematical Physics},
  year={2021},
  volume={383},
  pages={1559-1667}
}
  • Jiajie ChenT. Hou
  • Published 1 October 2019
  • Mathematics
  • Communications in Mathematical Physics
Inspired by the recent numerical evidence of a potential 3D Euler singularity \cite{luo2013potentially-1,luo2013potentially-2}, we prove the finite time singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup solution for the 3D Euler equations and the singular solution considered in \cite{luo2013potentially-1… 

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