Helmholtz's vorticity transport equation with partial discretization in bounded 3-dimensional domains

Reimund Rautmann and Vsevolod Solonnikov

Abstract: We prove the existence of a unique classical solution $w$ to the initial value problem of Helmholtz's vorticity transport equation with partial discretization in a smoothly bounded 3-dimensional domain for each bounded interval of time. The solution $w$ depends continuously on its initial value and, in addition, fulfills a discretized form of Cauchy's vorticity equation.

Keywords: Helmholtz's and Cauchy's vorticity equations with a discretization in H{ö}lder spaces; quasi-Lipschitz conditions.

Classification (MSC2000): 35A05, 35A35, 34A40, 34A12, 76C05.

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