THE NONLINEAR HODGE-NAVIER-STOKES EQUATIONS IN LIPSCHITZ DOMAINS
Résumé
We investigate the Navier-Stokes equations in a suitable functional setting, in a three-dimensional bounded Lipschitz domain, equipped with "free boundary" conditions. In this context, we employ the Fujita-Kato method and prove the existence of a local mild solution. Our approach makes essential use of the properties of the Hodge-Laplacian in Lipschitz domains.
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