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    Séminaire MAC

    Long-time strong sobolev instability for quasilinear NLS equations

    par Felice Iandoli

    → Europe/Paris
    Description

    A celebrated result by Colliander, Keel, Staffilani, Takaoka, and Tao (Invent. Math 2010) establishes the existence of solutions to the cubic nonlinear Schrödinger (NLS) equation on the two dimensional torus with arbitrarily small initial data and arbitrarily large growth of high Sobolev norms over long, but finite, time intervals. This phenomenon is nowadays often referred to as long-time strong Sobolev instability. In this talk, we show that the same phenomenon occurs for a class of Hamiltonian quasilinear NLS equations arising in the modeling of capillarity effects in compressible fluids. The proof is based on a combination of normal form techniques and paradifferential calculus. Based on joint work in progress with Y. Cacchio, F. Giuliani, and R. Scandone.