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This is a Quantitative Study study.

October 19, 2025Open Access

The Stokes problem with Navier boundary conditions in irregular domains

Key Points

Maximal regularity estimates for Stokes equations are established, enhancing understanding of fluid behavior under specific conditions.
Key results reveal that a single additional derivative is necessary for local boundary charts compared to no-slip conditions.
The study incorporates irregular domains, which allows exploration of real-world fluid scenarios with varying boundary conditions.
Proposed examples illustrate the sharpness of results and support the theoretical findings, providing a solid foundation for further research.

Abstract

Abstract We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces W^1, p W 1, p and W^2, p W 2, p for 1 1 p ∞ for the velocity field) in bounded domains of minimal regularity. Interestingly, exactly one derivative more is required for the local boundary charts compared to the case of no-slip boundary conditions. We demonstrate the sharpness of our results by a propos examples.

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Cite This Study

Breit et al. (Sat,) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc6970e5 https://doi.org/https://doi.org/10.1007/s00526-025-03141-z

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