pith:KYC67GB7
Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity II: 3D Profiles, Blowup, and Limiting behavior
The 3D incompressible Euler equations without swirl admit exact C^{1,α} self-similar blowup profiles for every α below 1/3, which are reached asymptotically from C_c^α initial vorticity.
arxiv:2605.15130 v1 · 2026-05-14 · math.AP
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Claims
For any α ∈ (0, 1/3), we construct exact C^{1,α} self-similar blowup profiles for the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from C_c^α initial vorticity and C^{1,α}∩L^2 initial velocity. Moreover, as α→(1/3)^-, the spatial blowup rate diverges while the profile converges to a nonzero multiple of r^{1/3} W̄_{1/3}(z).
The fixed-point map defined from the 1D approximate profile is a contraction in the chosen anisotropic weighted space, and the subsequent finite-codimension stability holds in the low-regularity C^{1,α} topology; both rely on the integration-by-parts identity along trajectories that exploits the Euler equation twice.
Constructs C^{1,α} self-similar blowup profiles for 3D Euler without swirl for α<1/3 and proves asymptotically self-similar blowup with limiting factorization to a 1D profile as α approaches 1/3 from below.
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| First computed | 2026-05-17T21:40:25.631995Z |
|---|---|
| Last reissued | 2026-05-17T21:57:18.952131Z |
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | unsigned_v0 |
| Schema | pith-number/v1.0 |
Canonical hash
5605ef983f0f5f15be8bec7454fa614b9a0e0b7a728d0bf72ff36c6583753cad
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