Multilinear estimates for the 2D and 3D Zakharov-Rubenchik systems
speaker: Carlos Matheus Silva Santos ( CNRS)abstract: The 2D and 3D Zakharov-Rubenchik (ZR) systems are dispersive Hamiltonian PDEs modelling the interaction of low amplitude high frequency waves with low frequency (acoustic type) waves. Besides its intrinsic physical relevance, the interest of the ZR systems resides in the fact that it includes the usual Zakharov system (which in turn generalizes the nonlinear Schrodinger (NLS) equations). Compared to the NLS and Zakharov equations, the ZR system presents an extra technical difficult: the symbol of the linear dispersive Schrodinger-type part may be non-elliptic, what makes the study of its well-posedness in low regularity more hard. In 2005, Jean-Claude Saut and Gustavo Ponce analysed this equation (based on a previous work of J.M. Ghidaglia and J.C. Saut about Schrodinger-type equations with non-elliptic symbols) and they were able to conclude local well-posedness in Sobolev spaces including strictly the energy space (associated to the natural Hamiltonian). In particular, they obtained only weak global solutions.
timetable:
Thu 15 Oct, 18:00 - 19:00, Aula Dini
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