Pith Number

pith:TUALTWL7

pith:2026:TUALTWL7SFNPXBLZUFDYESCOWG

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On Variational Approximations For Wave Maps

Changyou Wang, Zhiyuan Geng

Global weak solutions for wave maps into spheres exist as singular limits of minimizers to time-weighted elliptic functionals.

arxiv:2605.17536 v1 · 2026-05-17 · math.AP

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Record completeness

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Claims

C1strongest claim

The existence of global weak solutions of wave maps from R^n into S^{L-1} satisfying Box u perpendicular to T_u S^{L-1} is established as a singular limit of maps minimizing elliptic regularized variational functionals containing an exponential weight in the time direction with small parameter ε.

C2weakest assumption

The paper assumes that the minimizers of the ε-regularized functionals exist for each ε > 0 and that a suitable compactness or convergence argument as ε → 0 produces a limit satisfying the wave map equation and the initial data in the weak sense (abstract, paragraph on the singular limit construction).

C3one line summary

Global weak solutions for wave maps from R^n to S^{L-1} are recovered as singular limits of minimizers of exponentially weighted elliptic regularized functionals with initial data as boundary conditions.

References

10 extracted · 10 resolved · 0 Pith anchors

[1] De Giorgi,Conjectures concerning some evolution problems 1996

[2] Freire,Global weak solutions of the wave map system to compact homogeneous spaces.Manuscripta Math 1996

[3] A. Freire, S. Müller,M. Struwe,Weak convergence of wave maps from(1 + 2)-dimensional Minkowski space to Riemannian manifolds.Invent. Math. 130 (1997), no. 3, 589-617 1997

[4] A. Freire, S. Müller,M. Struwe,Weak compactness of wave maps and harmonic maps. Ann. Inst. H. Poincaré C Anal. Non Lin´daire 15 (1998), no. 6, 725-754 1998

[5] S. Múller, M. Struwe,Global existence of wave maps in I+2 dimensions for finite energy data. Top. Merhods Nonlinear Anaiy.sis, Vol. 7, 1996, pp. 245-259 1996

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:04:44.530492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d00b9d97f915afb8579a14782484eb1af76c7904ae04ce1fb9df64799736b44

Aliases

arxiv: 2605.17536 · arxiv_version: 2605.17536v1 · doi: 10.48550/arxiv.2605.17536 · pith_short_12: TUALTWL7SFNP · pith_short_16: TUALTWL7SFNPXBLZ · pith_short_8: TUALTWL7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TUALTWL7SFNPXBLZUFDYESCOWG \
  | 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: 9d00b9d97f915afb8579a14782484eb1af76c7904ae04ce1fb9df64799736b44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f6b6146cfd2b59181147c7df10aeca366c25de654300bfec2601e3da83e0eac",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T16:41:41Z",
    "title_canon_sha256": "20052dbb137cb37f7fb79bd4374d9edeffcdadad3207215c269e0b08c885ff46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17536",
    "kind": "arxiv",
    "version": 1
  }
}