Well-posedness of the unconstrained tangential-wall closure

Determine whether the two-dimensional incompressible Navier–Stokes problem for flow over a circular cylinder remains well-posed and physically meaningful when the no-slip condition is removed and the wall tangential velocity and its normal derivative are obtained from one-sided extrapolation of the interior solution.

Background

The paper studies viscous flow over a circular cylinder while retaining no-penetration but removing the prescribed no-slip condition for the tangential velocity. In the resulting numerical treatment, the wall tangential velocity and its normal derivative are extrapolated from nearby interior values and evolve with the flow rather than being imposed externally.

Because this closure differs from standard no-slip and prescribed partial-slip laws, the authors explicitly question whether the resulting boundary-value problem has a mathematically well-posed formulation and whether its solutions retain physical meaning. The simulations provide numerical observations but do not establish well-posedness or physical validity in general.

References

Whether the resulting problem remains well-posed and physically meaningful is not immediately clear.

— Is No-Slip Necessary for Vorticity Generation and Shedding over a Circular Cylinder?  (2609.00531 - Ghalejooghi et al., 1 Sep 2026) in Section 2, Problem Formulation

Whether such necessity for quantitative accuracy persists at high $Re$ requires further investigation.

— Is No-Slip Necessary for Vorticity Generation and Shedding over a Circular Cylinder?  (2609.00531 - Ghalejooghi et al., 1 Sep 2026) in Section 4, Results and Discussion