Cubic nonlinear Schrodinger equation on three dimensional balls with radial data

Ramona Anton

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Cubic nonlinear Schrodinger equation on three dimensional balls with radial data

Ramona Anton

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Abstract

We prove wellposedness of the Cauchy problem for the cubic nonlinear Schrodinger equation with Dirichlet boundary conditions and radial data on 3D balls. The main argument is based on a bilinear eigenfunction estimate and the use of $X^{s,b}$ spaces. The last part presents a first attempt to study the non radial case. We prove bilinear estimates for the linear Schrodinger flow with particular initial data.

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Ramona Anton. 2006-08-28. Cubic nonlinear Schrodinger equation on three dimensional balls with radial data. https://arxiv.org/abs/math/0608689

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