Finite-time Type-I blowup is proven for 3D incompressible Euler equations with initial data in C^{1,α} (α < 1/3) in the axisymmetric no-swirl class, using a Lagrangian clock-and-strain framework that yields explicit blowup rates.
Chen,On the singularity formation of the 3D Euler equations withC 1,α velocity, arXiv:2309.00150 [math.AP] (2023)
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The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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Incompressible Euler Blowup at the $C^{1,\frac{1}{3}}$ Threshold
Finite-time Type-I blowup is proven for 3D incompressible Euler equations with initial data in C^{1,α} (α < 1/3) in the axisymmetric no-swirl class, using a Lagrangian clock-and-strain framework that yields explicit blowup rates.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.