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We consider an anisotropic model case for a strictly convex domain ofdimension $d\geq 2$ with smoothboundary and we describe dispersion forthesemi-classical Schr{\"o}dinger equation with Dirichlet boundary condition. Morespecifically, we obtain the following fixed time decay rate for the linearsemi-classical flow : a loss of $(\frac ht)^{1/4}$ occurs with respect to theboundary less case due to repeated swallowtail type singularities, and isproven optimal. Corresponding Strichartz estimates allow to solve the cubicnonlinear Sch\"odinger equation on such a 3D model convex domain, hencematching known results on generic compact boundaryless manifolds.

Dispersive estimates for the Schr{\"o}dinger equation in a strictly convex domain and applications