## Preprint 2012-01

## Gabriel N. Gatica, George C. Hsiao, Salim Meddahi, Francisco J. Sayas:

### On the dual-mixed formulation for an exterior Stokes problem

### Abstract:

This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & N'ed'elec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the well-known Babuv ska-Brezzi theory: in particular, the well-posedness of the formulation will be established.

This preprint gave rise to the following definitive publication(s):

**Gabriel N. GATICA, George C. HSIAO, Salim MEDDAHI, Francisco J. SAYAS: ***On the dual-mixed formulation for an exterior Stokes problem*. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), vol. 93, 6-7, pp. 437-445, (2013).