Effects of velocity-dependent apparent toughness on the pre- and post-shut-in growth of a hydraulic fracture

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We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in t ...

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Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

2024

Quantitative convergence rates for scaling limit of SPDEs with transport noise

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