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The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions

PDE and Applied Math Seminar

Speaker: Jason Murphy, UC Berkeley
Location: 3106 MSB
Start time: Thu, Nov 12 2015, 4:10PM

In this talk, I will discuss recent joint work with R. Killip and M. Visan on the cubic-quintic nonlinear Schr\"odinger equation with non-vanishing boundary conditions in three space dimensions. In particular, we construct global solutions with prescribed scattering states. Our arguments build on work of Gustafson, Nakanishi, and Tsai on the related Gross--Pitaevskii equation. The presence of the energy-critical (quintic) nonlinearity and changes in the geometry of the energy functional add some new difficulties to the problem.