Quasi-Lipschitz conditions in Euler flows

In mathematical models of incompressible flow problems, quasi-Lipschitz conditions present a useful link between a class of singular integrals and systems of ordinary differential equations. Such a condition, established in suitable form for the first-order derivatives of Newtonian potentials in R-n (Section 2) gives the main tool for the proof (in Sections 3-6) of the existence of a unique classical solution to Cauchy's problem of Helmholtz's vorticity transport equation with partial discretization in R-3 for each bounded time interval. The solution depends continuously on its initial value and, in addition, fulfills a discretized form of Cauchy's vorticity equation.