Pith Number

pith:4OUCB3GU

pith:2026:4OUCB3GUM5OTJH4XDQYZGLKXN4

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Multi-Dimensional Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics

Jin Jia, Tao Luo

Mixed Riemann configurations with centered rarefaction waves and discontinuities remain structurally stable for the 2D isentropic Euler equations.

arxiv:2603.14696 v2 · 2026-03-16 · math.AP

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Claims

C1strongest claim

We prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as shock waves or vortex sheets), by deriving simultaneous energy estimates for acoustic and vorticity waves within the rarefaction wave region without loss of derivatives.

C2weakest assumption

The reduction of corner-region problems to Cauchy problems on the plane with periodic data and a single discontinuity line at t=0 assumes that the nonlinear superpositions can be controlled by the chosen initial data on Σ₀ without additional compatibility conditions that might fail in general geometries.

C3one line summary

Proves multi-dimensional structural stability of mixed Riemann configurations containing centered rarefaction waves and discontinuities for the 2D isentropic compressible Euler equations.

References

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[1] Alinhac, Existence d’ondes de raréfaction pour des écoulements isentropiques , Séminaire sur les équations aux dérivées partielles 1986–1987, Exp 1986

[2] Alinhac, Existence d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels, Comm 1989

[3] Alinhac, Unicité d’ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels , Indiana Univ 1989

[4] S. Benzoni-Gavage, and D. Serre, Multi-dimensional Hyperbolic Partial Differential Equations , Oxford University Press 2007 2007

[5] Stevens, Short-time structural stability of compressible vortex sheets with surface tension, Arch 2016

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Receipt and verification

First computed	2026-05-17T23:39:15.761417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3a820ecd4675d349f971c31932d576f13b969d83a724415bfcd699c5b4f6474

Aliases

arxiv: 2603.14696 · arxiv_version: 2603.14696v2 · doi: 10.48550/arxiv.2603.14696 · pith_short_12: 4OUCB3GUM5OT · pith_short_16: 4OUCB3GUM5OTJH4X · pith_short_8: 4OUCB3GU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4OUCB3GUM5OTJH4XDQYZGLKXN4 \
  | 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: e3a820ecd4675d349f971c31932d576f13b969d83a724415bfcd699c5b4f6474

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "189c570b65ba27492e38e2c459580a157968b3b054c3639a789d98ee927e2698",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-03-16T01:05:08Z",
    "title_canon_sha256": "9ba69c0162d782b93719e4a021cee9b154ee9abfa445feaa9af21fb760e2596a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.14696",
    "kind": "arxiv",
    "version": 2
  }
}