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Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity I: $C^{\infty}$ 1D Limiting Profiles

Jiajie Chen

For the critical case α=1/3 a C∞ self-similar blowup profile with unbounded stream function is constructed for a 1D model of 3D axisymmetric Euler.

arxiv:2605.15149 v1 · 2026-05-14 · math.AP

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Claims

C1strongest claim

For α = 1/3 we impose a crucial normalization and construct a C^∞ self-similar blowup profile with unbounded 1D stream function and infinite spatial blowup rate, using a fixed-point argument around a numerically constructed approximate profile.

C2weakest assumption

The numerically constructed approximate profile is sufficiently close to an exact solution so that the fixed-point argument converges in the chosen function space; the abstract does not quantify the approximation error or the contraction constant.

C3one line summary

Constructs C^∞ self-similar blowup profiles for 1D models of 3D Euler at α=1/3 using fixed-point around a numerical approximation, plus nearby exact profiles for α slightly below 1/3.

References

46 extracted · 46 resolved · 1 Pith anchors

[1] An introduction to numerical analysis 2008
[2] Smooth imploding solutions for 3D com- pressible fluids 2025
[3] Blowup for the defocusing septic complex-valued nonlinear wave equation inR 4+1.To appear in Commun 2024
[4] Global smooth solutions for the inviscid SQG equation 2020
[5] Singularity formation and global well-pos edness for the generalized Constantin–Lax–Majda equation with dissipation 2020

Cited by

1 paper in Pith

Self-similar blow-up solutions of incompressible Euler equations in $\mathbb R^d, d\geq 3$ with $C^{1,1-2/d-}$ velocity
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First computed 2026-05-17T21:40:25.488777Z
Last reissued 2026-05-17T21:57:18.806430Z
Builder pith-number-builder-2026-05-17-v1
Signature unsigned_v0
Schema pith-number/v1.0

Canonical hash

a4421da2685ee19e84ed49ecda3dc1815957722b3e1bb478c80b48d614763148

Aliases

arxiv: 2605.15149 · arxiv_version: 2605.15149v1 · pith_short_12: URBB3ITIL3QZ · pith_short_16: URBB3ITIL3QZ5BHN · pith_short_8: URBB3ITI
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curl -sH 'Accept: application/ld+json' https://pith.science/pith/URBB3ITIL3QZ5BHNJHWNUPOBQF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a4421da2685ee19e84ed49ecda3dc1815957722b3e1bb478c80b48d614763148
Canonical record JSON 
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    "submitted_at": "2026-05-14T17:50:19Z",
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