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.
Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen,Math
6 Pith papers cite this work. Polarity classification is still indexing.
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math.AP 6years
2026 6verdicts
UNVERDICTED 6roles
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If a mild solution to 3D incompressible Navier-Stokes with v0 in Ḣ^{1/2} and Ω0 in L^{r0} (r0∈(1,2)) blows up at T*, then for any 2<p<∞ and unit vector e the integral ∫_0^{T*} ||(v(t)|e)||_{Ḃ^{1/2+2/p}_{2,∞}}^p dt diverges at T*.
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.
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Stochastically forced Navier-Stokes equations interacting with an elastic structure
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.