Vanishing viscosity limit for an expanding domain in space
Variable depth KdV equations and generalizations to more nonlinear regimes
We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes, Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account...
Variational problems on classes of rearrangements and multiple configurations for steady vortices
Variations of Robin capacity and applications.
Vertical blow ups of capillary surfaces in . I: Convex corners.
Vertical blow ups of capillary surfaces in . II: Nonconvex corners.