English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the three-dimensional incompressible Euler equations on a boundeddomain $\Omega$ with $C^3$ boundary. We prove that if the velocity field $u \inC^{0,\alpha} (\Omega)$ with $\alpha > 0$ (where we are omitting the timedependence), it follows that the pressure $p \in C^{0, \alpha} (\Omega)$. Inorder to prove this result we use a local parametrisation of the boundary and avery weak formulation of the boundary condition for the pressure, as wasintroduced in [C. Bardos and E.S. Titi, Philos. Trans. Royal Soc. A, 380(2022), 20210073]. Moreover, we provide an example illustrating the necessityof this new very weak formulation of the boundary condition for the pressure.This result is of importance for the proof of the first half of the OnsagerConjecture, the sufficient conditions for energy conservation of weak solutionsto the three-dimensional incompressible Euler equations in bounded domains.

H\"older regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains