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Session S37 - New Developments in Mathematical Fluid Dynamics

Thursday, July 15, 11:00 ~ 11:25 UTC-3

Analysis of Incompressible Navier--Stokes Equations with Navier Boundary Conditions

Siran Li

New York University Shanghai, China   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We are concerned with the mathematical analysis of the Navier--Stokes equations in 3-dimensional domains for incompressible fluid dynamics. The Navier boundary condition, first proposed by Claude-Louis Navier, is a physical correction of the homogeneous zero boundary condition, which states that the tangential components of the stress induced from the fluid particles in the normal directions are proportional to the tangential components of the fluid velocity. We analyse the "geometric" regularity criteria of Navier--Stokes under the Navier boundary condition based on the alignment of vorticity directions, as well as the higher-order estimates for the vanishing viscosity boundary layer expansions.

Joint work with Gui-Qiang G. Chen (University of Oxford, UK) and Zhongmin Qian (University of Oxford, UK).

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