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Diffusive slowdown in miscible viscous fingering. (English) Zbl 1184.35260

The authors consider gravity-driven flows in a porous medium with initial conditions close to unstable stratification. They prove a refined upper bound on the size of the mixing layer in a simplified model of miscible fingering that quantifies diffusive slowdown. The studied system is a multi-dimensional system of hyperbolic conservation laws that admits an exact one-dimensional closure for which the Lax entropy condition is not physically appropriate. The proof is based on a study of dynamic scaling in mixing layer and on a construction of comparison functions that are viscous shock profiles for Burger’s equation.

MSC:

35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
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