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Investigate singularity formation and finite-time blowup in a quasi-exact one-dimensional model approximating the three-dimensional axisymmetric Euler and Navier–Stokes equations.

January 22, 2024NonlinearityOpen Access

Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes

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Authors

THThomas Y. HouCalifornia Institute of Technology YWYixuan WangBeijing University of Technology

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Implication

Theoretical study demonstrates finite-time blowup in a quasi-exact 1D fluid dynamics model, suggesting potential mechanisms for singularity formation in 3D Navier–Stokes equations.

Key Points

Investigate singularity formation and finite-time blowup in a quasi-exact one-dimensional model approximating the three-dimensional axisymmetric Euler and Navier–Stokes equations.
Analyzed the 1D Hou–Li model capturing competition between advection and vortex stretching across inviscid and viscous settings.
Conducted exact computations for low-frequency Fourier modes and derived leading-order damping estimates for high frequencies using singularly weighted energy norms.
Constructed a combined energy norm coupling singularly weighted norms with high-order Sobolev norms to control viscous instabilities.
Demonstrated that the inviscid model develops self-similar blowup under weakened advection with smooth initial data or under original advection with Hölder continuous data.
Proved that the viscous model with weakened advection and smooth initial data develops a finite-time blowup.

Cite This Study

Hou et al. (2024) studied this question.

synapsesocial.com/papers/6a08de0973760a4edcd605fc https://doi.org/10.1088/1361-6544/ad1c2f

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Implication

Theoretical study demonstrates finite-time blowup in a quasi-exact 1D fluid dynamics model, suggesting potential mechanisms for singularity formation in 3D Navier–Stokes equations.

Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes

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Implication

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Cite This Study

Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier–Stokes

Discussion

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Implication

Key Points

Cite This Study

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