Weak Compactness Methods for Singular Penalization Problems with Boundary Layers
Laure Saint‐Raymond · SIAM Journal on Mathematical Analysis · 2009
This paper is devoted to the study of large-scale oceanic motions forced by some wind at the surface and braked by solid friction at the bottom. As the effect of the Coriolis force is dominant, this is a typical singular penalization problem set in a bounded domain, which has been already studied by filtering methods in [N. Masmoudi, Comm. Pure Appl. Math., 53 (2000), pp. 432–483] or [A.-L. Dalibard and L. Saint-Raymond, J. Differential Equations, 246 (2009), pp. 2304–2354], for instance. We propose here an alternative “weak compactness” method, based both on compensated compactness arguments [I. Gallagher and L. Saint-Raymond, Handbook of Mathematical Fluid Dynamics, S. Friedlander and D. Serre, eds., Elsevier, New York, 2007] and on some 2-scales analysis [G. Allaire, SIAM J. Math. Anal., 23 (1992), pp. 1482–1518] and [G. Nguetseng, SIAM J. Math. Anal., 20 (1989), pp. 608–623]. It characterizes only the limiting mean motion but requires much less explicit computation and thus, should be extended to more complex models.