Global Existence for the Zakharov system
A talk in the Geometric Analysis Seminar series by
Timothy Candy
| Abstract: | The Zakharov system is a system of coupled Schrödinger-wave equations which was originally derived as a model in plasma physics. We show that in dimensions d>3 for large wave data, and small Schrödinger data, solutions to the Zakharov system exist globally in time and scatter. Moreover, we extend the regularity region for well-posedness to the sharp region. The key step is to prove a Strichartz estimate for the Schrödinger equation with a potentially large free wave potential. In contrast to previous work on the Zakharov system, we avoid the use of normal forms, and instead work with spaces which are carefully adapted to control bilinear interactions between solutions to the Schrödinger and wave equations. Avoiding the use of normal forms allows us to consider data with regularity in the extended full region of local well-posedness. This is joint work with Sebastian Herr and Kenji Nakanishi. |