Schrdinger-Poisson-Slater方程驻波的强不稳定性

Strong instability of standing waves for the Schrdinger-PoissonSlater equation

本文研究Schr¨odinger-Poisson-Slater(SPS)方程i?ψ?t+△ψ-χ(|x|-1*|ψ|2)ψ+|ψ|p-1ψ=0,χ>0,x∈R3.当p73时,运用变分法证明SPS方程的基态驻波强不稳定,并进一步用基态驻波解刻画SPS方程的解在有限时间爆破的门槛初始条件;在p=73时,建立了基态驻波解的L2范数的下界.

This paper concerns the Schr6dinger-Poisson-Slater （SPS） equation Via a variational argument, it is shown that the ground state standing waves are strongly unstable by blowup when p ~ 7. The sharp threshold of the initial dada for the global existence and blowup of the Cauchy problem for the SPS equation is established in terms of the ground state when p 7〉3. r This result implies a lower bound 7 for the L2 norm of the ground state standing wave solutions to the SPS equation with p = 7/3.