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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.01748 |
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Sommario:
- Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each point of the boundary $\partial D$. The previous existence proof relying on the Nash-Moser iteration scheme is replaced by an adaptation of Kato's approach to locally coercive problems, allowing a more precise statement: the regularity required in Sobolev spaces is the one needed to ensure a basic local coercivity property, and there is a loss of control of only two derivatives in the obtained solutions. The underlying variational structure gives an additional property: the obtained solutions are local minimizers of an integral functional. The strategy of proof is first developed for a simpler nonlinear partial differential equation in two variables which satisfies a weaker form of ellipticity.