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.
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1, 193–248, DOI 10.1007/BF02547354 (French)
15 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
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.
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.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
Constructs crossed-product von Neumann algebras M_u from incompressible flows to define commutator-based tracial complexity functionals linked to determinants and entropy.
Develops a recursive finite-window audit chain framework with anti-phantom certificates and propagation theorems for Navier-Stokes generated packages.
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.
Closes a gap in Wiegner's theorem by establishing non-algebraic decay for 2D Navier-Stokes solutions.
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.
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.
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.
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.
The paper is a memorial tribute collecting reminiscences of Robert V. Kohn's exemplary life and contributions to mathematics.
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Non-Algebraic Decay for Solutions to the Navier-Stokes Equations
Closes a gap in Wiegner's theorem by establishing non-algebraic decay for 2D Navier-Stokes solutions.