{"total":15,"items":[{"citing_arxiv_id":"2606.28131","ref_index":13,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Stochastically forced Navier-Stokes equations interacting with an elastic structure","primary_cat":"math.AP","submitted_at":"2026-06-26T14:32:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Global strong pathwise well-posedness established for stochastically forced 2D incompressible Navier-Stokes coupled to 1D damped Kirchhoff plate via velocity continuity and stress balance on fixed interface.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Nonlinear stochastic FSI problems on moving domains were then studied by Tawri and Čanić [59], who proved the existence of martingale solutions for a 2D Navier-Stokes fluid coupled to an elastic lateral wall. Further developments include stochastic FSI models with nonzero longitudinal displacement [58] and Navier-slip boundary conditions [57]. In three spatial dimensions, Breit, Mensah, and Moyo [13] obtained martingale solutions for an incompressible Navier-Stokes fluid interacting with a Koiter-type shell subject to transport noise. All these works construct solutions in aweak PDE sense. For an overview of deterministic and stochastic FSI problems, we also refer to the recent monograph [14]. We now describe the stochastic problem. Let(Ω,A,P)be a probability space endowed with a filtration"},{"citing_arxiv_id":"2606.27560","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Filtered Vortex Stretching and Subgrid Defects for the Three-Dimensional Navier-Stokes Equations","primary_cat":"math.AP","submitted_at":"2026-06-25T21:33:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Establishes a finite-scale estimate for filtered vortex stretching in 3D Navier-Stokes bounded by vorticity direction defects, absorbed by filtered diffusion, with far-field and commutator terms controlled via Carleson embeddings and cylindrical Young measures.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.25341","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A Structural Audit of Navier-Stokes Obstruction Calculus","primary_cat":"math.AP","submitted_at":"2026-06-24T03:13:24+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":3.0,"formal_verification":"none","one_line_summary":"Audit of Navier-Stokes obstruction calculus shows existing decompositions locate CKN badness transport but lack coercive estimates, proving a resolution lemma and identifying the need for a filtered stretching-diffusion estimate with subgrid terms.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.25322","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Coarse-Grained Resolution and Pressure-Flux Work Depletion for Navier-Stokes CKN Badness","primary_cat":"math.AP","submitted_at":"2026-06-24T02:38:56+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The paper establishes a coarse-grained resolution inequality Psi(r) <= 4 Psi^ell(r) + 4 Omega^ell(r) and a fixed-chain depletion theorem for combined pressure-flux work in the Navier-Stokes CKN setting.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.21783","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Finite-Chain CKN-Bad Scale Counting for Navier-Stokes: Standard PDE Closure and Canonical Detector Realization","primary_cat":"math.AP","submitted_at":"2026-06-19T22:11:40+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Proves a finite-chain CKN-bad scale counting theorem for 3D Navier-Stokes via standard PDE closure with one-component compactness and an amended canonical detector realization.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.20899","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Finite-Window Recursive Audit Chains for Navier-Stokes Generated Packages","primary_cat":"math.AP","submitted_at":"2026-06-18T19:52:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Develops a recursive finite-window audit chain framework with anti-phantom certificates and propagation theorems for Navier-Stokes generated packages.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.18476","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Finite-Window Local-to-Clean Transfer and Anti-Phantom Detection for Sharp Navier-Stokes Packages","primary_cat":"math.AP","submitted_at":"2026-06-16T20:36:39+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":3.0,"formal_verification":"none","one_line_summary":"Proves a local-to-clean detection theorem and anti-phantom principle ensuring baseline-visible defects in sharp Navier-Stokes packages are either detector-caught or charged to a quotient-residual ledger under listed conditions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.12756","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Invisible Defect Cascades for Navier-Stokes Regularity","primary_cat":"math.AP","submitted_at":"2026-06-10T23:52:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"The paper presents a conditional scale-critical defect-cascade reduction for the local regularity problem of the 3D incompressible Navier-Stokes equations that excludes invisible cascades to obtain CKN-scale regularity under structural hypotheses.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.12267","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Schur Visibility and Anti-Phantom Reduction in One-Component Navier-Stokes Degeneration","primary_cat":"math.AP","submitted_at":"2026-06-10T16:11:09+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Proves the standard observable package is insufficient for quantitative trace rates in NS one-component degeneration and states a conditional dichotomy on relaxed Schur visibility versus an NS-realizable left-singular cascade.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.11720","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Strict 2.5D Shadows for One-Component Navier-Stokes Regularity","primary_cat":"math.AP","submitted_at":"2026-06-10T06:50:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Proves a conditional finite-scale reduction theorem deriving a lower bound on the regularity radius from smallness of the vertical velocity component under multiple structural assumptions for 3D Navier-Stokes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.08352","ref_index":1,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Finite-Scale One-Component Regularity via Harmonic Pressure for the 3D Navier-Stokes Equations","primary_cat":"math.AP","submitted_at":"2026-06-06T21:55:30+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Under a fixed scale-invariant bound on suitable weak solutions of 3D Navier-Stokes, smallness of the vertical velocity component yields a positive lower bound on the local regularity radius via harmonic pressure approximation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.09306","ref_index":258,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Weyl asymptotic formulas in the nilpotent Lie group setting","primary_cat":"math.FA","submitted_at":"2026-05-10T04:02:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.02117","ref_index":26,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Robert V. Kohn (1953-2026)","primary_cat":"math.HO","submitted_at":"2026-05-04T00:44:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"The paper is a memorial tribute collecting reminiscences of Robert V. Kohn's exemplary life and contributions to mathematics.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"During the PhD, Bob met with me at least once per week-sometimes two or three times-either telling me to come on in to his office when I stopped by, or taking out his pocket book to pencil in another time. Meetings were both therapeutic and lively. One time, I explained a mess of calculations that seemed to go nowhere involving the Jin-Kohn entropy method [26] and a problem in elasticity. Bob smiled and said, \"Well, you learned something.\" Another time, I was supposed to have prepared to present a paper of his on the shape of leaves and flowers, but came with notes about crumpled cylinders instead. Bob simply pivoted and asked me to explain what I was thinking about. Bob brought a zen-like atmosphere to doing mathematics and taught me that if one thing didn't work"},{"citing_arxiv_id":"2604.17917","ref_index":2,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Crossed-Product von Neumann Algebras for Incompressible Navier--Stokes Flows and Spectral Complexity Indicators","primary_cat":"math.OA","submitted_at":"2026-04-20T07:53:41+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Constructs crossed-product von Neumann algebras M_u from incompressible flows to define commutator-based tracial complexity functionals linked to determinants and entropy.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"u(x, t) of period 1, for which the Poincar' e map Φ = Φ1,0 is well-defined and measure-preserving. For general non-autonomous Navier-Stokes fields u(x, t), one must replace the Z-action by an evolution cocycle/groupoid framework (Section 3.6). 1.3 State of the art and the \"supercriticality barrier\" Leray's foundational work established global weak (finite-energy) solutions in 3D, but uniqueness and reg- ularity remain open in general [2]. A frequently emphasized difficulty is supercriticality with respect to scaling: the a priori bounds naturally available for Leray solutions are not scale-invariant in 3D, and classical compactness/energy methods do not prevent concentration at small scales (see e.g. [14, 15] for an expository discussion). At the same time, there exist striking global regularity results for special large-data classes,"},{"citing_arxiv_id":"2512.21312","ref_index":8,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Non-Algebraic Decay for Solutions to the Navier-Stokes Equations","primary_cat":"math.AP","submitted_at":"2025-12-24T18:15:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Closes a gap in Wiegner's theorem by establishing non-algebraic decay for 2D Navier-Stokes solutions.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}