Abstract
We consider the solution of the Stokes problem at a corner between a free surface and an inflow or outflow boundary. A formal asymptotic solution for the dominant contribution to the streamfunction near the corner is derived. We give a heuristic discussion of the relevance of the nature of the corner singularity to the formulation of well-posed boundary value problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. R. Dean and P. E. Montagnon,On the steady motion of viscous liquid in a comer. Proc. Cambridge Phil. Soc.45, 389–394 (1949).
P. Grisvard,Elliptic Problems in Nonsmooth Domains. Pitman 1985.
H. K. Moffatt,Viscous and resistive eddies near a sharp corner. J. Fluid Mech.18, 1–18 (1964).
M. Renardy and Y. Renardy,On the nature of boundary conditions for flows with moving free surfaces, (to appear J. Comp. Phys.)
V. A. Solonnikov,On the Stokes equation in domains with non-smooth boundaries and on viscous incompressible flow with a free surface. InNonlinear Partial Differential Equations and their Applications. Collège de France Seminar, Vol. III. (Eds. H. Brézis and J. L. Lions), pp. 340–423, Pitman 1982.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Renardy, M. Corner singularities between free surfaces and open boundaries. Z. angew. Math. Phys. 41, 419–425 (1990). https://doi.org/10.1007/BF00959988
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00959988