Construction of blow-up solutions for Zakharov system on T2

摘要

We consider the Zakharov system in two space dimension with periodic boundary condition:{i?_tu=-Δu+nu,?_(tt)n= Δn+Δ|u|~2,(t,x)∈[0,T)×T~2. We prove the existence of finite time blow-up solutions of (Z). Further, we show there exists no minimal mass blow-up solution.