2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100415We show that unstable fingering patterns of two dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the KdV hierarchy. In this framework, the fingering instability is linked to a known instability leading to regularized shock solutions for nonlinear waves, in dispersive media. The integrable structure of the flow suggests a dispersive regularization of the finite-time singularities.Published versionMesoscale and Nanoscale PhysicsSoft Condensed MatterHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext