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math.AP2018
Existence of a lens-shaped cluster of surfaces self-shrinking by mean curvature
Pietro Baldi, Emanuele Haus, Carlo Mantegazza
We rigorously show the existence of a rotationally and centrally symmetric "lens-shaped" cluster of three surfaces, meeting at a smooth common circle, forming equal angles of 120 d…
math.AP2018
Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation
Marcel Guardia, Zaher Hani, Emanuele Haus +2
We consider the defocusing cubic nonlinear Schrödinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori ca…
math.AP2018
On the existence time for the Kirchhoff equation with periodic boundary conditions
Pietro Baldi, Emanuele Haus
We consider the Cauchy problem for the Kirchhoff equation on with initial data of small amplitude in Sobolev class. We prove a lower bound $\varepsilon…