微分方程式セミナー


2017/6/30(Fri)

16:30--18:00 数学教室 大セミナー室(E301)

Jason Murphy

University of California, Berkeley

Random data final-state problem for the mass-subcritical NLS in $L^2$

We study the final-state problem for the mass-subcritical NLS above the Strauss exponent. For $u_+\in L^2$, we perform a physical-space randomization, yielding random final states $u_+^\omega\in L^2$. We show that for almost every $\omega$, there exists a unique, global solution to NLS that scatters to $u_+^\omega$. This complements the deterministic result of Nakanishi, who proved the existence (but not necessarily uniqueness) of solutions scattering to prescribed $L^2$ final states.