Quasi-Lipschitz conditions in euler flows

Abstract

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 (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 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.