MathDB3 problems
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The attractor conjecture for arbitrary-connectivity Laplacian growth
In Laplacian growth, the interface evolves under zero-surface-tension dynamics, and a nonsingular solution is one that remains free of singularities during the evolution. In the si…
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The surface-tension-free pattern-selection conjecture for arbitrary-connectivity Laplacian growth
Laplacian growth is interface evolution driven by Laplacian fields, including Hele-Shaw flow, and the domain may have arbitrary connectivity. Surface tension is assumed to be small…
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The zero-surface-tension selection conjecture for arbitrary-connectivity Hele-Shaw flows
A Hele-Shaw flow describes viscous fluid motion in a narrow cell, and its connectivity is the connectivity of the fluid domain. Surface tension is neglected, so the interface evolv…