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Boundary singular sets for Stokes equations. (English) Zbl 1034.35088
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker (ISBN 0-8247-0672-2/pbk). Lect. Notes Pure Appl. Math. 223, 167-177 (2002).
For Stokes equations, the authors study relations between the size of removable singular sets on the boundary and their removability. After proving that the capacity function belongs to a fractional Sobolev space, the author demonstrate that singular sets with sufficiently small capacity are removable to fractional Sobolev solutions. Then the fact that Poisson kernel for Stokes equations maps the capacity measures on the boundary to a suitable fractional Sobolev space in the whole domain allows the authors to formulate a removability criterion in terms of capacity of singular sets for sufficiently regular Sobolev solutions.
For the entire collection see [Zbl 0972.00046].
35Q30 Navier-Stokes equations
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows