{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:W4CBVMNYT4L7XUGVRAYVXSICEP","short_pith_number":"pith:W4CBVMNY","schema_version":"1.0","canonical_sha256":"b7041ab1b89f17fbd0d588315bc90223ee4bd70bb9a5f11b091b652702b0cefe","source":{"kind":"arxiv","id":"2605.10849","version":2},"attestation_state":"computed","paper":{"title":"Well-posedness of a generalized Stokes operator on domains with cylindrical ends via layer-potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Under positivity assumptions on V and V0 the generalized Stokes operator Ξ and its layer potentials become invertible on domains with cylindrical ends.","cross_cats":["math-ph","math.DG","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Mirela Kohr, Victor Nistor, Wolfgang Wendland","submitted_at":"2026-05-11T16:59:02Z","abstract_excerpt":"We study the \\emph{generalized Stokes operator} \\begin{equation*} \\bsXi \\ede \\bsXi _{V,V_0} \\ede \\left(\\begin{array}{ccc} \\bsL + V & \\nabla \\\\ \\nabla^* & -V_0 \\end{array}\\right) \\end{equation*} on a \\emph{domain with straight cylindrical ends} $\\Omega$ using \\emph{the method of layer potentials} on $M \\supset \\Omega$. The operator $\\bsXi_{0, 0}$ is the classical Stokes operator. Under suitable positivity assumptions on $V$ and $V_{0}$, we prove that $\\bsXi$ is Fredholm. This allows us then to define the single- and double-layer potentials $\\bsS$ and $\\frac12 + \\bsK$. Under further positivity a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.10849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-11T16:59:02Z","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP"],"title_canon_sha256":"18e568f8a6096c1141cc6acd903a0488197b1b9ef4ab7048700d6b624dbaa1c7","abstract_canon_sha256":"c48f9d673bec10a544cb96e9d8a6a4153d643a8600c486b53b8c1589fbef4e7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:46.414866Z","signature_b64":"voVK6E+215PMl2jTqIgxyov25rPvIQXVyfhv7mKq797vmrvuhnNyCUA/RrnseujR8CRfVJYr5WqdYU7s0ULHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7041ab1b89f17fbd0d588315bc90223ee4bd70bb9a5f11b091b652702b0cefe","last_reissued_at":"2026-05-29T02:05:46.414071Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:46.414071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well-posedness of a generalized Stokes operator on domains with cylindrical ends via layer-potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Under positivity assumptions on V and V0 the generalized Stokes operator Ξ and its layer potentials become invertible on domains with cylindrical ends.","cross_cats":["math-ph","math.DG","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Mirela Kohr, Victor Nistor, Wolfgang Wendland","submitted_at":"2026-05-11T16:59:02Z","abstract_excerpt":"We study the \\emph{generalized Stokes operator} \\begin{equation*} \\bsXi \\ede \\bsXi _{V,V_0} \\ede \\left(\\begin{array}{ccc} \\bsL + V & \\nabla \\\\ \\nabla^* & -V_0 \\end{array}\\right) \\end{equation*} on a \\emph{domain with straight cylindrical ends} $\\Omega$ using \\emph{the method of layer potentials} on $M \\supset \\Omega$. The operator $\\bsXi_{0, 0}$ is the classical Stokes operator. Under suitable positivity assumptions on $V$ and $V_{0}$, we prove that $\\bsXi$ is Fredholm. This allows us then to define the single- and double-layer potentials $\\bsS$ and $\\frac12 + \\bsK$. Under further positivity a"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under slightly stronger assumptions on V and V0, we prove the invertibility of the operators Ξ, S, and ½ + K. The invertibility of these operators leads to well-posedness results for the associated (linear) Stokes boundary value problem with Dirichlet boundary conditions on Ω. As an application, we prove the well-posedness result for the Dirichlet problem for the generalized Navier-Stokes system with small data on a domain with cylindrical ends.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Under suitable positivity assumptions on V and V0, we prove that Ξ is Fredholm. Under further positivity assumptions, we prove that S and ½ + K are also Fredholm. 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The invertibility of these operators leads to well-posedness results for the associated (linear) Stokes boundary value problem with Dirichlet boundary conditions on Ω. As an application, we prove the well-posedness result for the Dirichlet problem for the generalized Navier-Stokes system with small data on a domain with cylindrical ends.","one_line_summary":"A generalized Stokes operator on cylindrical-end domains is Fredholm and invertible under positivity assumptions on V and V0 via layer potentials, yielding well-posedness for linear Stokes and small-data Navier-Stokes Dirichlet problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Under suitable positivity assumptions on V and V0, we prove that Ξ is Fredholm. Under further positivity assumptions, we prove that S and ½ + K are also Fredholm. 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