Random data final-state problem for the mass-subcritical NLS in 𝐿²

Murphy, Jason

doi:10.1090/proc/14275

Random data final-state problem for the mass-subcritical NLS in $L^2$
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Proc. Amer. Math. Soc. 147 (2019), 339-350 Request permission

Abstract:

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, which proved the existence (but not necessarily uniqueness) of solutions scattering to prescribed $L^2$ final states.

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