Random Data Final-State Problem for the Mass-Subcritical NLS in L²
We study the final-state problem for the mass-subcritical NLS above the Strauss exponent. For u+ ∈ L2 , we perform a physical-space randomization, yielding random final states (formula presented). We show that for almost every ω, there exists a unique, global solution to NLS that scatters to (formula presented). This complements the deterministic result of Nakanishi, which proved the existence (but not necessarily uniqueness) of solutions scattering to prescribed L2 final states.
J. Murphy, "Random Data Final-State Problem for the Mass-Subcritical NLS in L²," Proceedings of the American Mathematical Society, vol. 147, no. 1, pp. 339 - 350, American Mathematical Society, Jan 2019.
The definitive version is available at https://doi.org/10.1090/proc/14275
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2019