• Corpus ID: 247614661

Asymptotic self-similar blow up profile for 3-D Euler via physics-informed neural networks

  title={Asymptotic self-similar blow up profile for 3-D Euler via physics-informed neural networks},
  author={Yongjian Wang and Ching-Yao Lai and Javier G'omez-Serrano and Tristan Buckmaster},
We develop a new numerical framework, employing physics-informed neural networks, to find a smooth self-similar solution for the Boussinesq equations. The solution corresponds to an asymptotic self-similar profile for the 3-dimensional Euler equations in the presence of a cylindrical boundary. In particular, the solution represents a precise description of the Luo-Hou blow-up scenario [G. Luo, T. Hou, Proc. Natl. Acad. Sci. 111(36): 12968–12973, 2014] for the 3-dimensional Euler equations. To… 

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